>>956453Start doing training hikes with anything you've got. Even if it's just running shoes, a nalgene, and a wind-breaker. Do half-day hikes, then full-day hikes. Get altitude as much as you can, even if that means taking a weekend to drive somewhere that has altitude.
You'll find that with what you've got that there's "something that could be better about..." or "this thing I had didn't work..." or "I really wish I would have had..."
When ever you find yourself saying/thinking something like that as a result of your hikes, you'll know what you need to buy or start researching.
As you start getting into multi-day hikes you'll need to start somewhere with a tent and sleeping bag. Try and find used gear from good brands. You'll find yourself saying the same things as above, and that's the impetus for you to sell what you have and buy something that better suits your needs.
If you make 2-3 trips /out/ per week and do the above you'll find that you quickly have the gear you need.