You'll be fine with whatever you have, just fit a new chain of the right length. Pretty much every rear dérailleur ever made can cope with at least a 28t big sprocket (nominal max on some Shimano is 27, but they really go to about 30 on most frames) and at least 28t total capacity, so as long as your chain ring difference is no more than 15t (e.g. 53/38) it's hard to see what there has ever been which won't cope.
@gbj_tester started
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You'll be fine with whatever you have, just fit a new chain of the right length. Pretty much every rear dérailleur ever made can cope with at least a 28t big sprocket (nominal max on some Shimano is 27, but they really go to about 30 on most frames) and at least 28t total capacity, so as long as your chain ring difference is no more than 15t (e.g. 53/38) it's hard to see what there has ever been which won't cope.