Congrats on your purchase! how fun to have your own private outdoor space. If you provide the measurements and what part of the world you live in or garden zone, you will get better ideas :)

Oh, so cute! It will be fun! And congratulations on the new home!🎉🍾🏠 Do you want a small dining table, or just some chairs? Fire? A colorful outdoor rug is a good start. Does it get enough sun where you may need an umbrella? Are you allowed to paint the fence?

I’m not living there yet, so I can’t get exact measurements but I believe the fence is about 10 feet and then the garage is about 13 feet. I live in western New York as well.

Unfortunately, I cannot paint the fence as it’s maintained by the HOA. I would definitely like seating and a table. I’m a little nervous about having fires back there so no fire pit. We do get a lot of sun in the afternoon so I absolutely want an umbrella

Maybe something like this? (I covered part of the fence with rolled reed fencing; don't know if that would be allowed. That inspired a somewhat Asian treatment of the space.)

And a plan view:

Do you use the fence gate?

Incidentally, I used 12'x15' above as the patio area dimensions. (Two graph paper squares equal a foot.) If the fence boards are 1x6's, counting them gives at least 12' (probably closer to 14'; 31 boards times 5 1/4" plus the small spaces between boards) as the length of the fences. Longer dimensions would make the space less tight than shown. You'll want to measure before you buy furnishings!

My first priority, before doing anything else, would be to deal with the hardscape. Assuming your HOA gives you free rein regarding that, I would remove or resurface what’s there. If that’s not in the budget either powerwash it & get a large outdoor area rug or have it stained or repainted with concrete paint. I’ve also seen very thin pavers that are installed over concrete , eliminating the demo of the existing surface. BTW,it doesn’t appear that the HOA is doing a very good job of maintaining the fence, perhaps ask them to restain it.