If you have any tool skills at all, you can make your own bench for bench presses. When I started weight training, my father and I built our own like this:
Get a wooden board of about 2 m x 30 cm x 5 cm, or whatever width fits you.
(not wider than your back between your shoulders)
Saw off two pieces of about 15-20 cm, which you'll then attach to the main board with long screws, these are the feet.
Sand off any splinters and use a folded woolen blanket as padding - you're done.
Plus, this will easily fit in a corner or under the bed.
This and a set of dumbbells and a long weight was all the equipment we needed to exercise any muscle we wanted. You'll get good results doing bench presses with the dumbbells and pushups.

Just remember to exercise your back and shoulders, too. For example you can incline the bench by putting one end securely on a chair, lie face down on it, and pull the weights off the floor towards your shoulders.
You should have a training partner for spotting and motivation, don't forget to stretch before training!