For 0W-20, I like Mobil 1's 0W-20. It's my default recommendation for 0W-20 because it's a known good/great oil, relatively easy to find, relatively inexpensive, etc. It also has a slightly higher HT/HS viscosity (2.7 cP vs. standard for the grade 2.6 cP) and excellent cold cranking viscosity. Not that it necessarily matters in Texas, but it demonstrates that it uses very good base stocks.
The only reason that Mobil 1 0W-20 isn't in both of my vehicles now is I got the oil that I am using for super cheap.
For 5W-20, I still like Mobil 1, but other brands are more widely available in this grade, like Pennzoil Platinum, Castrol Syntec, Quaker State Ultimate Durability, Valvoline SynPower, etc. You can get all or most of these brands in 0W-20, but it's harder to find for some.
Use whatever grade the oil cap/owner's manual indicates.