Not to rez a dead post, but I grew up in Lampasas (an hour NW of Austin) and moved back a few years ago. I got into hunting recently as an adult, but I don't fish.
If you want to hunt cheaper locally, the main way to go is to put in for the Parks and Wildlife Drawn Hunts. That'll get you in the game pretty cheap, but obviously it's not guaranteed. It's hard to find decent leases where I live now for working-man wages. I've had my eye on a few locally, and one up at Caprock Canyons. The main things with the drawn hunts is quite a few of them are very remote, and the climate can be very harsh from extreme heat to extreme cold. Fort Hood also allows public hunting for certain things, and they have their own process of obtaining access.
I have a lease now out in Crockett County, which is about 4 hours west of where I live, and it's affordable for what I earn, and it's low fence.