House Indoor plants

I am getting into indoor plants...my outdoor don't seem to want to grow in this heat. So..If I buy an indoor plant...in a 3" pot...can I leave it in that pot and the intention being it won't grow much? I know that if I trim the growth (at the top) I can keep it from getting to tall, but being in that small pot...it is only a small space for the roots to expand...if they don't expand...do they rot? Do they die? I want an arrangement on my window sill and in some glass decorative containers I have in the house...But I want them to stay small. I will transplant them into a nicer small pot instead of those plastic ones they come in..but.... I want them to stay small, but still grow and be green! Any suggestions?