Seems that you may be a little recoil sensitive. Not to worry. Lots of people are. If shooting larger cartridges bothers you, by all means don't force yourself to do it. I'm not real sure a 30-30 is going to help much in a situation like this. Your idea of going to a smaller caliber sounds logical, and I'm sure you will want to compare the recoil of several gun/cartridge combinations to see what you best can live with. .243's are generally adequate guns in the hands of an adequate shooter. Bullet type and placement are critical, as with nearly everything else. I would suggest that you may want to try something in between the .243 and the 30-30, such as a .257 Roberts, .260 Rem., or 7mm-08. Recoil should seem noticeably less to you than the '06 or .270.
Just gives you more reasons to spend more time at the range
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