You are not expected to have a weapon at your first event, or even for your first several events. Weapons are expensive and are a big investment. A M1 Garand, M1903 Springfield, or war-made M1 Carbine start roughly at $650. A Thompson, M3 Grease Gun, sniper rifle, or Browning Automatic Rifle can run you into the thousands.
The basic standard for our unit would be the M1 Garand. Quite possibly the best source of M1 Garands would be the Civilian Marksmanship Program. There are certain hoops one must jump through in order to buy from the CMP, but the price and quality assurance generally cannot be beat. If you are lucky enough as to be close to either of their physical locations, stop by, even if to only gawk. We also may have one or two extras laying around for sale as well - you never know with this bunch.
After the M1 Garand a M1 Carbine or M1903A3 Springfield would do fine. Pistols are a must if you do Mounted Recon, but only truly appropriate for NCOs, Officers, and gun crews (mortars, MGs, etc.).
Caring for one's weapon is extremely important. Not only are you caring, most likely, for a piece of history that is worth hundreds of dollars,