I'm looking to put a new 7 speed cassette on my Shimano 600 Tricolor equipped steel road bike. The goal is to achieve some lower gearing for hills (the bike came used with a 12-21 cassette, and 40/52 chain rings). The offerings around town seem to be variations of the Shimano HG50 7 speed cassette with either 12-28, 13-28, 13-30, 13-34 etc. options.
I've heard different opinions from different local bike shop mechanics about which cassettes are compatible with my bike. One suggested the 13-30, and didn't seem to think there would be any issues with rear derailleur capacity. Another mechanic suggested that I wouldn't want to go with any rear cog larger than 28, and if I still needed lower gearing I should consider swapping out my smaller chain ring.
So my question is, what is the actual capacity of my rear Shimano 600 tricolor derailleur?
Further than that, are there mechanical reasons to prefer a 28 tooth cog with a smaller chain ring for lower gearing over a 30 tooth or 34 tooth largest cogs?