Jack is right that it's almost certainly cheaper to buy used than build your own, but this sounds like a good beginner project (depending on the design). Even if you don't get power tools, all the little things like levels, measuring tape, framing square etc. add up in a hurry so there's a fair initial investment, but you'll want those things anyway now that you own a place.
Since it's probably a fairly small piece, you might be able to get wood for it from someone's leftovers/cutoffs from a bigger project for cheap. E.g., 2x6 decking, or pine tongue and groove panelling, could work for parts of it. Or you could build it from scrap, weathered wood for a rustic look.
You could design the project in such a way as to skip some of the tools. E.g., you could just use screws to fasten it together from the inside, and not need pocket screws or joinery, or if you do the weathered/rustic look then nails through the top would fit right in.
I think the really essential things would be:
Framing square
Drill + bits - set of drill bits, and a red Robertson driver bit (a countersink bit if you would be fastening any screws on the outside)
Some kind of saw - circular saw probably has greatest utility, or even a jigsaw, which would allow you to make curved cuts. Theoretically you could even use a handsaw, but it takes some skill.
Screws (no. 8 Robertson to match your driver)
And, as Jack said, your PPU - safety glasses, ear protection if you are using power cutting tools, and a good respirator (don't get the disposable dust masks, those are just silly.) If you are not sanding and you can do all your cutting outside the respirator isn't so critical but you'll probably find there are lots of tasks you want it for anyway.
Clamps are really handy but you can get by without them if using screws. You may not need a sander depending on the wood/style/design. If you won't have food or anything on it you also may not need to finish it (or you can just use an oil-based finish, like walnut oil, rubbed in with a rag.) A measuring tape is a pretty all-around useful tool you'll want to have anyway (but you still need a framing square for the edge and for the 90 degrees).
Check out ana-white.com for great simple project plans.