Joined: Aug 2010
Posts: 12,717
Likes: 2,104
From: Madison, WI
Bikes: 1961 Ideor, 1966 Perfekt 3 Speed AB Hub, 1994 Bridgestone MB-6, 2006 Airnimal Joey, 2009 Thorn Sherpa, 2013 Thorn Nomad MkII, 2015 VO Pass Hunter, 2017 Lynskey Backroad, 2017 Raleigh Gran Prix, 1980s Bianchi Mixte on a trainer. Others are now gone.
Sram makes a 12-32 seven speed cassette, but if you have a biggest sprocket of 28 at this time, it is possible that your rear derailleur would have to be replaced to install a 32.
If you can put a 24T chainring in front, 32T biggest sprocket in rear, that will get you up most hills. That is what I have on my bike in the photo above. I am guessing you can do that with your existing crankset.
A new cassette before a long trip with a new chain is always a good idea anyway.
I assume you are content to stick with seven speed, eight or more means new shifter (or at least rear shifter) and likely a new rear hub or wheel, possibly rear derailleur.