You fear your rabbit 'will soon get depressed'? What does that even mean? Lots of rabbits live alone very well. Some don't but if he didn't, you'd know. My Aki can't live alone: she was alone twice, for about one month when I first got her and for about 2 months when her first husbunny died. During those periods, she was never ever laying down or relaxing, always moving, constantly jumping on my knees and back on the ground, she developped OCD and was so nervous she was litteraly shaking all the time. That's a rabbit that can't live alone.
About the cost, I never had rats. Though, I did hesitate between that and rabbits and one of my friend had several. Rats develop tumors and breathing problems after 1 year and a half to 2 year. That's almost unavoidable from what I've read and heard. If you treat them, the cost will be a lot worse than for a bunny. There is no such thing as a cheap pet. If you feed them correctly and that you go to the vet when needed, all animals are potentially expensive. If you don't have the money, you shouldn't have a pet at all - rehome your rabbit and wait until you're in a better place to care for an animal.