A Rega P2 or P3, Goldring GR1 or Moth (all Rega-made) are the easiest in terms of zero adjustments. Buy a Rega Elys, Super Elys or Exact and there's no alignment, either, Just set the tracking weight and play. Had a P2 for years and loved it. A classic.
Personally, I love the Technics SL-1200. Very easy to set up. No alignment when you buy a KAB cartridge (www.kabusa.com) because it just plugs in. Try the KAB-Ortofon Pro S40. I think it's worth investing an extra hour learning about setup because the Technics is really a great table, too. Buy it from KAB and Kevin will talk you through the whole setup process.
Either table is great...and once you adjust them, they stay adjusted. No maintenance on either.
