Being another 'sensitive' guy, those calibers stated above make me flinch just reading them! I can say that the above posters that are steering you towards the 308 parent cartridges are giving the straight goods. The 243, 7-08, 308 are all in my comfort zone. The upper end of calibers for me is the 30-06.
My advice from one sensitive guy to another is to buy a quality rifle that has the proper weight to caliber ratio,( light rifles have more 'felt' recoil than the heavier versions), with an excellent trigger. Stay away from the 'mountain' versions until you're used to a bigger punch.