I think it's kinda cool to shoot bullseye with basic, fixed sight 1911s. You ain't gonna run any real aces off the line with one, but it will improve your overall shooting immensely and it's all kinds of fun. Having your gun perfectly zeroed will go a long way toward making it an even more enjoyable experience.
Personally, I'd pick a load and carefully zero the gun to it and the longest distance I expected to shoot. The only things required are a hammer, drift punch, file and a bottle of cold blue. Do your zeroing from a solid rest and then shoot the gun again from your normal shooting position to confirm.
FWIW, I have found that Winchester 'white box' 230 grain ball or JHP, and a 200 grain LSWC over 5.0 of W231 (1.250 OAL) shoot real close to each other all the way to 50 yards.