I don't know how you guys play this game but I absolutely suck at it. It takes me ages to get up on my feet (clothes-wise) before I can actually start doing any of the interesting stuff, and then as soon as I get any momentum going, something always seems to happen which kills me and it's all over again.
I'm no expert at the game - in fact, most of my time is spent blundering about and getting by on luck - but here are some tips:
Head to the 'glow' right at the start.
Make a sling and fill your pockets with rocks.
Kill everybody you come across while heading to the glow.
Take all their shit. Stop and scavenge here and there. If it says you alerted nearby people, run. Don't scavenge busted up buildings - you're asking to get hurt.
If you see a dogman, run. Literally hit run on the in-game screen; you can't do this if you got a cart, though. If you can't run, hide and cover your tracks.
If you have to fight it, pray you kill it with your sling. If you can't kill it, run some more. If you can't run, die.
Once you make it to the 'glow', the safest thing to do is treat it as your 'hub' from which you can adventure out, find stuff, and return to heal up/restock.
From there you can safely start exploring the story - but I'd start avoiding combat if at all possible. Fighting people at the start makes sense as you need their things, but later on it's usually not worth your time unless you need some resources. Combat is intended to kill you. No matter how 'badass' your character is one slip up can be your doom. So I'd suggest avoiding it if you can. But there's a bit of redundancy in that statement - later in the game you'll be so tough-looking that most wastelanders will avoid you. In that case, you get to pick your fights more often than not. This also allows you to more or less safely begin scavenging the wasteland as you no longer have to worry about other people dropping in on you.
Also, my personal tip is to get 'diagnostic' checks done every so often if you can, especially if you've been in some trouble lately. Realizing you're sick with something lets you treat it and head it off. The game simulates sickness somewhat accurately: you can be sick without realizing it. Your symptoms give it away, but by that point the damage has been done and if it's something super serious you're probably fucked.