Since it's your first time, don't sweat what us experienced players say. You will be using stimpaks on your first playthrough because this game throws surprises at you all the time.
Sneak isn't critical to play the game. Just helpful in some cases.
About the skills: most people opt for Small Guns their first time playing because of their abundant supply. I recommend you invest in it as well, at least until you're more comfortable. The hunting rifle and combat shotgun are the best choices early. Sniping won't do you much good early on because your Small Guns skill will be low. However, its scope is invaluable when running through the Capital Wasteland. Use it to look ahead of the path you're on. You can either fight or get around.
As you level, enemies get stronger, so don't go shooting too much, as exp will grant you quick leveling. At level 10, the game's most feared enemy will be on the map, and that's the Deathclaw. Fast and can easily kill you.
Head to Megaton (if you didn't blow it up) and speak to Moira. She'll ask you to help her with a book, which gives you three quests to do. It helps get your feet wet and one quest will reward you well with your own sniper rifle.
If you still need guidance, let us know. We're always happy to help a new Fallout player! Woots! *pops Mt. Dew soda can
Cheers.