As @mattnz alludes to, this is a good time to think about what you like and what you don't like about your current drivetrain. Do you like the shifter type (e.g. trigger vs gripshift)? Do you like the action of your current shifters? Do you like your gear ratios?
You can certainly get by without changing anything other than the BB and crankset; in that case, you'll want similar tooth counts on the chainrings of a 3x crankset compatible with x9 rear cassette and chain.
You have an aftermarket crankset; BB technology has advanced since your square taper BB, and today's "external bearing" BBs are considered superior while similar in price. Many will actually thread into the same shells as the square taper BBs, and so are straightforward upgrades.
Shimano's Hollowtech II BBs perform well at reasonable prices, but there are other brands that will also fit you BB shell width and threading. Normally, one chooses a compatbile crankset/BB combo. With Hollowtech II, you can purchase an older new old stock or used higher end crankset and a new current Hollowtech II BB, or stick with a (fairly) current crankset like Shimano's FC-T4060 cranksets. The available tooth counts for the latter are either 44/32/22 or 48/36/26, so your rear derailleur should work fine with either (if you change your maximum tooth count or range too much, you may need a different RD to handle the new range).
Remember also that unless your chain and cassette are quite new, they will be somewhat worn; it's worth installing a new chain with the new crankset, and perhaps a new cassette as well.
PS - Photo of brass caliper (4") that costs about $5 at US home improvement stores.