You probably don't have any ammo because you shoot it up doing all those quests. Take your time and develop your ammo dealers and visit them every three days for a while: Tenpenny, Paradise Falls, Moria, Rivet City, Casdin at Ft. Indy, the caravans. Get your perception up so you can avoid fights not of your choosing. If you play the first ten or so levels as a fast paced shooter, you'll always be running low on ammo. A lot of fights aren't worth the ammo used to win them, but when you have to fight use stealth and sniping and make your first shot count.
There is enough junk laying around to finance a sizable portion of your ammo needs if you take the time to pick it up and haul it back to sell it, but as PW says, having enough caps isn't usually a problem.
All of this is easier if you use fast travel to the ammo dealers, but it's doable without it. By level 5 or so, my last character had finished Moria's book, had the A3-21, Lincoln's Repeater, Vengeance, Xuanlong Rifle, Ranger Armor, etc.
You should not kill the Mirelurks at Anchorage, you should sneak by them using the things Moira gives you. That place is scary, but if you can avoid the Lurks, it's a fun quest - and there's a lot of good loot in there.
Oh, and welcome to the forum.