If you're playing at home then yeah, get a small one first. Maybe even (and this may be blasphemous to some people) buy the game "Rocksmith 2014", it's immense fun and will keep you playing.
I have to admit that when I practise alone I do it not plugged into anything, at most I might use my bass attack into a computer and then listen on headphones, but the big thing for me is being able to hear the metronome or drum track.
Which leads me to the other thing. If you're on your own, get a metronome or drum machine app for your phone or an actual physical drum machine metronome. These are the best learning tools you can buy.
As to basses. It seems from what I hear the best bang-for-buck basses out there at the moment are the Sire Marcus Miller basses, but you might not like the "Fender Jazz" look.