You can sample GURPS Lite for free. GURPS Lite is basically just GURPS with a smaller shopping list, less detail, and no "advanced dials" turned on.
Reasons why GURPS is great for post-apocalyptic:
- Realistic radiation and disease rules if you want them.
- Unrealistic mutations can be point-balanced easily.
- Psionics rules if you want them.
- Species-building is easy. Robot-building is relatively easy.
- GURPS High-Tech is full of modern day hardware.
- Good combat system, but also has good interaction and professional skills to back it up, when you need them.
- Boring stuff, like foraging, holding down a day job, or building mundane items, is largely hand-waved.
- GURPS is set up quite nicely to freely mix improvised equipment, retro TL 4 gear, and modern stuff all using one rules-set. If you want to arm a party with a baseball bat, a zip fun, a hand-forged spear, and a shotgun, GURPS is your game.
- Useful stats for animals.
- If you want to later add "surprises" like magic, aliens, hidden pockets of TL 10 survivors, the fact they aren't actually on Earth, or time travelers, GURPS is very modular and friendly.