You don't need a fancy gym. Standard dumbbells and plates are fairly inexpensive and you can shove them under the bed when you're not using them. On the other hand, to 'do it all' (large/compound lifts otherwise done with barbell), you'd really want to look for Olympic dumbbell handles and plates (and really good or 'lockjaw' collars). Olympic plates you can find easily second-hand, but not Olympic dumbbells (much to my consternation; don't want to buy standard plates seeing as I have 500lbs of Olympic already lol). You should be able to get a decent setup for around $150 (Scour Craigslist for an even better deal), or 2-3 months of what the average gym would run you. You won't need as many plates starting out... few 5's, 10's and maybe a pair of 25's or 35's (or 'standard' equivalents). You won't need 45's for quite a time unless you also get a barbell (my personal favorite but you really can't isolate the arms/shoulders with them much, hence the dumbbells. And it's INCREDIBLY stupid to use a barbell without a bench/rack anyway, so don't until or unless you can get one or the other; and if/when you do, DON'T collar your barbell so you can ditch out if you need to. Never collared and it's saved my ass many a time... I lift alone).
Oh, and disturbingly, gyms are moving almost exclusively to machines or 'machine assist' (racks), from what I've been seeing (have to conclude it's over liability BS). That is a piss-poor way to do it. They don't, at-all, work your stabilizers (your deep muscles)... so you're essentially throwing away 50% of your effort and potential gains, right from the off. There's nothing a machine can do that you can't get done with free-weights, dumbbell or barbell. Free-weights are ALWAYS best... you just have to pay more attention to do it right/safe. Our local Fitness 19 being the absolute worst offender I've ever yet seen... I haven't used my $9 membership in a year over it. It disgusts me. The only thing they have there that I could actually benefit from, can't really have at home, are the roman chairs and dip stations. But that's about as far as their free-weights go. It's a total joke. My high school gym had nothing but free-weights; the way it really ought to be.