For just lowers, you pretty much don't need anything extra than what you've got, although I personally would use a 3 pin castle nut wrench (the one I like is the Tapco Enhanced stock wrench - cheap and makes tightening/loosening your castle nut easy) - and I also find a cheap spring loaded automatic center punch is handy for staking.
If you want to do uppers as well, I'd recommend at least a reasonable vise with halfway deep jaws and one you can put some force on without it breaking (the "heavy duty" (49.99) ones from Lowes are plenty good enough...and worth it over the 29.99 ones, a torque wrench (for the AR barrel nut, I personally prefer a cheap beam type wrench - as you are not working to an exact torque value I find beam is better to see roughly where you are in the range than a clicker - and you can also pick one up for about $20 or so), some barrel vise jaws (the $10 DPMS ones are fine) and an upper receiver action block (I personally prefer the DPMS panther claw type, YMMV). You already have a barrel nut/flash hider wrench. Think that is pretty much it for "essentials", if you can even call them that - other stuff I find myself using though are a torque screwdriver (Wheeler FAT wrench), some small spirit levels and a good metal ruler. You'd also be advised to have some loctite on hand (blue and red), and also some Moly grease for the barrel nut.
The best tool in your box however, is taking your time and learning all the little nuances of putting these things together - it really is very simple, but depending on your mechanical ability it would possibly pay you to really study some of the free guides available here and elsewhere on the 'net to really understand how the entire system works and where you need to be particularly careful etc.
Good luck with it all...but I warn you, once you start with this, there's no going back....you'll become obsessed with putting them together! :)