The steps you mentioned would be the first to consider, and will not introduce any compatibility issues except that you might need a longer chain.

For more serious hill climbing the next steps are a triple crank (lots involved there) and a cassette with even larger cogs like 32 or 34 teeth (new rear derailer.)

I would figure out what gears you want/need using a gear calculator and decide based on that. Just me guessing, a 34 ring combined with a 28T largest cog on the cassette should work with no other modifications and should give you all the gear you'll need.