First, get yourself a tent and a sleeping bag with an insulator. Hotels are expensive compared to a campsite so you want to go with that.
Second, DO NOT GO OUT DURING THE RAIN. Nothing more demoralizing than getting wet, even with a full on raincoat that makes you look like a cultist you'll feel like shit to return somewhere safe
Third, be wary of who is around you. Some people will be great people, others will think that you're a junkie trying to sell drugs. I had kids less than ten asking if I dealt with drugs.
Fourth, if you're hitchiking, be patient and do it somewhere close to civilization. You're gonna hate yourself when the sun sets and you're in the middle of nowhere and have to ask someone to send the cops because you're going crazy.
Fifth, you cannot walk a highway. Not in a million years. Not many will take you up there either.
Sixth, talk to people. The best experience of going outside is talking to people and realising that they're not fiends or ghouls but they actually want the best for you, and for themselves obviously. You learn with them, and they learn from you. You can also get yourself a free lunch and dinner if you get with the righteous ones.
Seventh, realize that the only way to go is forward. You may not know what lies ahead, but that makes it evermore thrilling.
Eight, you may carry more clothes that you may need. Sure it's good to have it at hand, but it takes space that could be used for some survival items if you ever decided to go to the wilderness.
Just hope that you're just having a stress/anxiety/panic attack induced event and not homeless due to problem with your parents OP. I had the former happen to me twice.