Welcome aboard. At some point, everyone here was new to the AR-15. Better to ask questions than find out the hard way.
1. what is a good AR ammo and a good grain (what does a higher grain vs lower grain numbers mean?)
Grain refers to the projectile weight. In simple terms overall shorter projectiles weigh less, overall longer projectiles weigh more. A projectile's grain weight and projectile shape are paired to the twist rate of a barrel and the purpose of your shooting.
How to Pair Barrel Twist Rates with Bullets | Guns & Ammo
For range practice, I'll buy the most affordable ammo which is usually 55gr.
2. what should I get? 5.56 and 2.23? or both?
That depends on your barrel's chamber. Check your barrel. It should have the caliber stamped on it. If it is not readily visible, reference your owner's manual to find out what your rifle's manufacturer explicitly states.
Simple rule of thumb:
5.56 chambered rifle = shoot both .223 Remington and 5.56 NATO
.223 chambered rifle = shoot only .223
Why?
While visually similar in outward appearance, there are differences in case construction and propellant charges. The 5.56 NATO cartridge produces higher pressures than .223 Remington cartridge. There is also a difference in the 5.56 NATO chamber and the .223 Remington chamber.
I also heard that you can only use certain ammo at certain ranges...
This issue arises mostly from the use of steel case, bi-metal jacket ammo typically of Russian manufacture. Where a traditional FMJ consists of a copper jacket, a bi-metal jacket projectile consists of a mild steel, copper washed, jacketed lead core projectile.
The reasons some ranges ban the use of Russian steel case, bi-metal jacketed ammo:
1. The mild steel jacketed projectile can spark against a backstop. This has the potential of igniting range dust at the backstop, causing a fire.
2. The backstop is damaged by the use of the mild steel jacketed projectile.
3. The range uses spent cartridges as a small extra source of revenue. Brass cases are usually reloadable. Steel cases are not. The labor to sort out the steel cases (even using a magnet) from the brass cases negates the cost/benefit of selling fired range cartridges to commercial ammo remanufacturers.
*** Keep this in mind when buying ammo. Some ranges do not allow commonly found "green-tip" 5.56 ammunition. This is 5.56 ammunition with a copper metal jacket with a steel penetrator tip.
Everything you wanted to know about steel case, bi-metal jacket v.s. brass case, copper FMJ is here. I suggest you read it later.
Brass vs. Steel Cased Ammo - An Epic Torture Test
3. buying local vs buying online? (I know prices are generally better online)--going to a gun show this weekend...is there good ammo sold at those shows?
There can be good ammo sold at gun shows, but the better question is at what price. The hard part of being new is calibrating your internal price barometer. Price is relative to the construction specs of the ammunition. The best way to start to calibrate your internal 5.56/.223 price barometer is to:
1. Go online to price out ammo.
2. Take the total cost of the ammo and divide it by the number of rounds. That will give you price-per-round difference. The price-per-round makes a difference as you buy greater quantities of ammo.
Remember to factor in total cost. Total cost = cost of ammo + shipping + tax.
3. Pay attention to the different ammo specs. Price is dependent on component material, country of manufacture, and purpose of use. Plinking ammo made in a former Soviet-Bloc country will be cheaper than super-accurate U.S. manufacture hunting rounds.
.... now that that's over....
Buy the plinking/practice ammo that will give you the most opportunity for trigger time, given your local range restrictions. After years of buying a few boxes of ammo here and there, I started to buy ammo by the case. It's a punch to the gut to spend that much on ammo in one shot, but the price-per-round drops.
If ranges near me did not prohibit the use of Russian steel case ammo, I would buy it. The spec of the Russian steel case bi-metal jacket ammo I will buy is 100% dependent on the construction details of the casing. I will buy:
1. Polymer coated steel case. An example is the TulAmmo typically found at Wal-Mart.
2. Zinc coated steel case.
I personally stay away from lacquer coated steel case ammo. The lacquer melts in the high heat of the chamber, causing a gummy residue in the chamber. That gummy residue can cause failures to extract. It's also a cumbersome chore to clean out.
Good luck. If you have any questions, just ask.