First of all get the biggest possible tank you can get. Small tanks are not good for fish or for fish owners- they are actually more work than bigger tanks because you have to do more frequent water changes.
Tanks are usually standard sizes and there are a lot that are 60cm wide- would that fit your gap? A 60cm tank is roughly 60 litres which is a perfect size for a first tank. Don't get anything less than 45 litres, it won't be suitable for fish. Don't get a biorb, a fluval edge or any of those 'lifestyle' type tanks, they are all overpriced crap. A plain old glass box like a clearseal or similar will be fine, or try a one with a built in filter like a Juwel.
Filters are a MUST! Don't bother with an undergravel, they went out in the 80s. An internal filter like a Fluval U2 would be just right for a 60 litre tank. Easy to maintain, also cheap and reliable. A heater will give you lots more options for fish and tropical fish are no harder to keep. In an unheated 60 litre tank you'll be limited to minnows, although they are lovely fish so not much of a big deal if you really want an unheated tank.
After setting up you will need to prepare the tank for fish. This can take 4-6 weeks. Do NOT put any fish in the tank during the preparation, despite what some people might tell you (yes, even the staff at the fish shop). Adding fish to the tank too early can cause illness or even death. Patience will pay off and avoid many potential problems. Full explanation here
You'll need a water testing kit to monitor the cycle and also to see what sort of water you have- your fish choice may be limited if you have really alkaline or really acidic water. A liquid test kit is more expensive to buy but better value in the long run. Try the API or Hagen mini master test kit. You need to be able to test for ammonia, nitrIte, nitrAte, pH and hardness.
Real plants are fab, there are lots of easy ones to grow. You'll need lighting and a fertiliser to go under the sand/gravel.
Sorry, that's a lot of info all in one go and probably makes it all sound very complicated. It isn't really, it takes a while to set up but if you do it right and choose the right fish then you'll just have to do one water change a week and that'll only take about half an hour or so.
If you want me to explain any of it in more detail just ask :)