I have a similar area: 950 square feet total.
I'm not real sure about the nice even spaces you mentioned. I'm a newbie but as I have researched I have discovered that different plants require different distances between them. All of that being said, here is what I have decided (maybe it will help?)
On the north east corner I have corn (4.3' x 19.5' = 50 stalks)
(between the beds and around the edge i have a 2' walking path)
To the north west I have beans (5.5'x6' = 9 bean poles) and against this bed I have peas in the north west corner (5.5'x9') - kinda forms an L with the bean bed
In front of the peas and beans (walk space inbetween) I have tomatos in an L shape (3.4'x6.9') + (6.1'x6.1) = about 6 or 9 tomato plants
To the east of that I have squash (7.7'x7.9') = 9 squash plants and more to the east I have another joined bed: southern peas - black eyed (9.7'x4.4'), and various peppers (5'x9.7')
In the south east I have a led of pickles and cucumbers and to the west of that, I will be planting all of my shorties.
I will try to get this on some sort of diagram or plan, but that is what I have spray painted in my yard right now.
I was surprised at how much I could fit into a 950' area - and still have space to walk through and around. I'm sure there are neater and more efficient ways (like the three sisters method) but I am new and wanted to keep it simple this year.
My note on watering: I will use a fancy system I call a "water hose" this year. All of my plant beds will be slightly raised but will not have borders or be a "raised bed". I might try to figure out how to rig in a drip system, but I've gotte figure out a way to do it cheap! Most likely, I will be standing in my back yard, enjoying an early morning pipe and coffee while moving the water hose around.
Good luck. I'll post a pic when I have one!