Galveston and Surfside are pretty flat and sandy. That's good for the trout fishing because it'll get green, but there's not much decent bottom structure to attract reds. You can still catch the occasional one here and there but I think your odds are lower.
Go North to High Island or South to Bryan Beach or Sargent. There's more clay and shell bottom around those parts that seem to attract the redfish. Bryan Beach is usually pretty hard packed sand all the way down to the MOB so it should be fine in a 2WD. Sargent can get dicey pretty quick, but you should be able to stake out a decent fishing spot from the beachside road that runs North from the swing bridge. I haven't driven High Island so no pointers from me there.
Redfish are structure oriented look for freshly cracked coquina shells, clay piles, current rips, and points on the beach. Any or all of them are good redfish signs. The more in one place the better.
You shouldn't need yaks to get to the reds, but in some cases it may not hurt to have a few rods deep. Usually you can reach them with rods casted to the 2nd and 3rd gut, and every once in a while they'll be in the first gut (offshore of the first sandbar). Stagger how far out your different rods are until you find where they're biting.
For tackle, you should be fine with a couple hundred yards of 15-20 lb mono and a 25 yd topshot of 40 lb, but I like 50 lb braid with about a 30-40 yds of mono for a little stretch. The longer the rod the better, but you're probably used to sandbar rub from shark fishing.
You didn't say that you were looking for a new rod/reel but here's a couple setups I'd recommend:
For about $100 you can do a 10 ft okuma longitude casting rod and a 6500 abu.
For about $200, I'd go with a 6000 penn battle and a 10-12 ft penn prevail spinning rod.
For leaders, I use 3 way swivels and 100 lb mono: 2 ft to a barrel swivel on the top, 18" to a 7/0 circle hook, and 2 ft to a snap for connecting to a 4-8oz spider weight. If there a sharks in the area and you're getting broken off you can go to wire. Sometimes the redfish are wire shy and sometimes they aren't.
For bait, mullet and whiting heads are my first choice because they hold up the longest. About fist length is a good size for bull reds. Once it cools down and the hardheads and crabs aren't so thick, I like to use large fresh shrimp (table quality) or live crabs cracked in half just before they go out. Don't forget that mullet over 12" have a season.
"May not take from public waters, or possess on board a boat, mullet over 12 inches during October, November, December, and January. No limits apply during other months."
Edit:
Leader pics here:
http://texags.com/forums/34/topics/2748494/2 
