Only had one suit before and it was tailored for me in HK. Obviously not an option here from a $ POV so what do I do? Just go to some store like MJ Bale, get one that vaguely fits and take it to an alterations shop?
Is there any part of the suit that can't be altered or anything else I need to watch out for?
Shoulders and chest cannot (easily) be altered, neither can sleeve width. So I'd recommend finding a suit where the jacket fits your chest and shoulders correctly.
You can then alter
The waist (belly) - you can let out a couple of centimetres usually, in case you find the perfect shoulder fit with a tight belly fit.
The sleeve length as long as the jacket has 'fake' sleeve buttons that can be moved up and down
Do not buy a jacket with working sleeve buttons, i.e. buttons and actual button holes, because then you cannot alter the sleeve length (without making a mess of the armhole/sleeve joint). This is a mistake i have made and pay the price for every day.
There's a lot more I don't know, keen to read others' replies.
Other advice:
Buy 100% wool for longevity, breathability and shape. Polyester suits get stuffy and have a more rigid shape. Warning if you get ultra fine wool like 'Super 120s', the fabric will wear out between your legs and result in awkward holes. A good tailor can patch that up with tougher material though. Your choice, fine wool does feel damn fine.