Hi, I'll attempt to offer some good advice on a couple of points.
1) "What would be the best way to set up the new tank to quickly acclimate my fish." If i'm correct that you are already at the new house, then i would set up the 38 gallon by adding water and dechlorinator and getting it to the same temperature as the smaller tank. Once it is up to temperature, then i would move as much filter material to the new filter, (or simply move the filter to the new tank) and put as many decorations and gravel into the new tank without cleaning anything. Then bag the fish in bags, set the bag in the new tank and leave it for half an hour. Then add a little water from the new tank to the bag, and let it sit for 10-15 minutes, then let the fish go.
2) "How would you recomend moving them." Try catching them in a bag or clear jar without touching them with the net. Try using the net to corral them into the bag or jar. I figure it's best not to touch the fish if you can help it. Once you have them bagged, just move them over as described above. If you have to drive them to some other location, put the bags in a box, or insulated cooler and make sure there is lots of air in the bags. There should be more air than water in the bag. Set up the new tank as described above, and make sure the water is near the same temperature before letting the fish go. Keep the filter material and decorations wet in some tank water for the move.
3) "What would be some nice tank mates. looking for a pleco of some sort." This is sort of a personal choice situation. If i were you i would start by adding more of your tetras to make each a group of 4 or 5, (ie add 3 black neons, and 4 lemons).
Good luck.
