Hello Dewey!
Welcome to the Long Range Hunting Forum!
To answer your question the calibres that are not effected by wind as much usually have higher Ballistic Co-efficients (Like Derek said).
The Ballistic Co-efficient is a measure of drag/air resistance on the bullet. Generally the heavier the bullet, as long as the shape of the bullet is aerodynamic (High BC), the further it can fly with less wind effect.
For example a Flat nosed 200gr (Sierra) .375 has a ballistic co-efficient (BC) of .195, compared to a 300gr(Sierra) .338 hollow point boat tail which has a BC of .768!
However, the hard hitting high recoil rifles are generally not a good starting point to hone your skills, play with these toys at the start and you may throw in the towel.
If you are starting of start with the .22 then work through to .223, 243, .270 etc. These will help adaption to recoil and get marksmanship sorted. I recommend the .22 to start with at 100yds it will react (wind wise) similar to a .308 at long range and help learn the wind, trigger control, breathing etc.
Even if you play with the long range rifles you need to learn wind reading/doping.
This is purely recommendation, it is much cheaper to learn lessons on the .22 than on a .338. Then when you get to the bigger fellas you will be able to rule out marksmanship over adjusting to recoil.
But as Derek said the .338's, .300's, 7mm's and 6mm/6.5mm are big long range contenders. Alot of people are opting for the smaller calibres with less recoil and higher BC's due to being able to keep your sight picture plus longer ability to shoot the rifle.
Hope this is helpful,
CZ