I'm glad to see some interest from another new gardener. As for me being the "guru", lol. this is just my 3rd year really being into gardening, I just read a lot.
I'm going to break your post into different topics.
1. New garden/tilling/compost/soil ammendments.
In a perfect situation, you would've broke ground end of last summer or into the fall. Maybe you did, maybe you didn't? Don't get your hopes up too high for a first year garden plot as it takes a few seasons to condition the soil, but don't let that stop you either. After removing all sod and tilling, wait a couple of weeks and test the soil ( I will get into tests later). You want the soil from the 4" deep mark to test so don't till too deep yet. Once you see where you are at with your N,P,K you can report that and I can help you with what to add to the soil or point you in the right direction as to sites etc that can help you (the places I go for info).
As for your compost- what is in it? There are many things that can be in compost, eamples- coffee grounds, grass clipping (do not compost grass clippings that have seeds on the top or you will be creating a monster) dried leaves from fall, straw, plants from prior gardens (lot's to learn about which plants to compost and which to destroy, but this is your first year so it shouldn't be a problem) kitchen scraps such as egg shells, lettuce etc. And most important is manure. I'm guessing no manure in your compost? You can buy manure, but watch the numbers on the back of the bag, if it's .01 it is dirt, look for higher. I buy a hummus/manure blend. Is your soil soft for the first few inches down and then clay? If so, peat moss is the cheapest way to loosen it. After your first soil test, till as deep as that tiller will allow and really blend that soil and manure and or your compost.
You can buy soil test kits at any nursery, Home Depot/Lowes, etc. Look for a 10 test kit, it should run roughly $20. You want this so you can test the first time, a couple weeks after adding to the garden, mid season, and then after season.
2. As for all that you want to plant in a 9'x12' area
One of the worst things a gardener can do is to crowd plant/overplant. Not only will it make your fruits and vegetables smaller and less of a harvest overall, it robs the soil of all nutrients. Example- What I did 2 seasons ago with all the melon plants in that small area. I was new to gardening and thought that since I could get all the vines and fruit off the ground by trellisin, I could plant a lot in that bed. BIG mistake. Last season corn is all that grew worth a darn, after testing the soil I learned I depleted all nutrient levels with all those melon plants and have been adding a lot to the soil for this year. OJ is right about Zukes, they are BIG plants. 3'x3' and up to 5'x5' is just one plant. Think about just one of those in your garden. As for the squash/zuke hybrid problem............ This is something I have researched quite a bit when I decided I wanted to cross 2 cantaloupe varieties, breed the hybrid out of it, and create my own variety (this takes some years to achieve and I will have to start all over). If you buy a hybrid zuke and hybrid squash plants and plant them next to eachother, you will not get a mutant hybrid fruit from them. If this happens, neither plant was a true hybrid, meaning first generation. They had been cross pollinated the year before and the seed that plant came from was a hybrid between the two fruits. Happens all the time, especially when plants are bought from big box stores. To further explain..... You get an OP (open pollinted or heirloom) zuke or sqash or even a true first generation hybrid that had to be hand pollinated indoors with NO bees or bugs around to cross pollinate and plant them together, a bee can take pollen from a male flower of one and pollinate a female flower of the other with that pollen. The fruit that grows will be true to what it is, but the seeds inside that fruit if planted the next season can produce mutant hybrids. ( sorry if this bores you, just wanted to explain so you wouldn't worry about this). To go a little further into this, the flavor of the fruits can be horrible from this happening in melons cross pollinated with anything from the curcubit family, but no issues with zukes and squash.
I suggest what OJ said about plants that climb aka trellis. On an edge of the garden you can build a trellis and put pole bean seed a few inches from it. They will grow and climb as long as 10 feet depending on variety. If you go with bush beans they stay low to the ground (why they are called bush) and take up valuable ground space. On another edge, build another trellis for cukes. What I am saying is that anythng that can be trellised should be when trying to save ground space like you will need to do if you want to plant most of what you want to. Google image trellis and add cucumber, bean etc in the description and you will get many ideas. Tomatoes are the most popular fruits in the garden, yes they are fruit and not vegetable. You have to figure out which varieties you want to grow when thinking of space needed. Example- A Brandywine plant may grow to 6' tall if supported and 4' wide where a Roma will be half of this size. Definitely use cages on your tomatoes and don't let them just crawl on the ground. That takes up too much space and many fruits rot. As for potatoes- Tomorrow I plan on planting mine. 2 weeks ago would've been better, but you can't do that when you get 9" of rain in 4-5 hours
I am just now able to work in the garden they are going into. Buy your seed potatoes and after you cut them you need to plant them 12-18" apart in rows and space rows atleast 30" apart. Expect full grown plants to be a 14-24" radius. They take up some space and you need to be able to hill them which takes up even more space. Peppers are along the same lines of what I mentioned for tomatoes.
I know this is a long winded post, but I get into this stuff and want to share with you what I have learned. If you don't mind, I'd like to make a suggestion...........
If you have to stay with the 9'x12' plot, don't plant the zuke plant unless you REALLY like zukes. too much space needed for the return in harvest, but don't get me wrong, you will get more than you and the wife can eat from just one plant if healthy. Figure 2 feet inbetween tomato plants and grow a few different kinds because they are easy to grow and are not too picky when it comes to soil nutients compared to other plants you listed. Look into trellising. Not just because I am a trellis freak, but for the reason of why I am a trellis freak, they save space. You can build them from tree branches to save money, old springs from bed mattresses, pvc like I do. The materials are endless. Just keep in mind the wind speeds of out summer storms and plan on a way to secure them to the ground.
If I were you this year with that space, I'd do a few tomato plants space 2 feet apart, a few peppers in the same way with cages also, if you want slicing cukes you can grow them in tomato cages also and can get away with a little less than 2 feet apart. Build one trellis on an edge of the garden for pole beans (Kentucky Wonder is a great one) and forget about taters this year.
I know you are a busy guy, but I'd also like to suggest a few sites and forums that have taught me 90% of what I have learned the past couple years.
www.thebayougardener.com This is the forum I am on most of the time. They are mostly Southern folks so planting dates vary from them to us, but the Southern hospitality on that forum is second to none. They also are huge fans of harmful pesticides so watch out for that.
www.helpfulgardener.com More people from the North and Eastcoast, but not as close knit of a forum. A member there " Jal-ut" is peobably the best cool climate gardener I have seen on the net. Watch out for the tree hugging "don't squash bugs" hippes on that site. Don't ever mention shooting a rabbit or groundhog there lol.
youtube. TONS of gardenening videos on youtube. One guy on there goes by the name of "web cajun" that is the man who owns the bayougardener site and he is pretty much the Godfather of youtube gardening videos. My personal favorite youtuber to watch videos and learn from goes by the name of MHPgardener. Bobby is his name and he is a member on thebayougardner forum. This guy is AMAZING!
Hope this all helps and if I give too much detail, let me know.
I will get some pics up this weekend and start my 2012 thread or threads for my gardens. I will get an accurate measurement of my gardens, number of plants and space devoted to them and hopefully that will help you before you plant the following weekend. Just to give you an idea of what is going on for me this year in the garden, RETURN OF PVC TRELLIS! This time smaller and for pickling cukes and very low tech and keeping cost down. I have had 64 Walla Walla onions in for I'm guessing 5 weeks or so (I have to look back for sure). A shorten growing season sweet corn. Potatoes and explaining weighing seed potato before planting so you can weigh your harvest to figure your return (you're a math teacher, right?) All of this along with cantaloupe and beans will be planted out by end of this coming weekend, possibly maters, peppers, and slicing cukes, but may wait one more week for those. I'm looking at another 48-52 hour work week, so I should have this all complete and up here Sunday.