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Would a max of USD 1k be a good budget ?

Absolutely! Thats way more than enough

I would probably recommend something like the Sony a6000 or the Canon M3!

I hear a lot of photographers talking about things like different lenses and filters. Should I be too worried about those for now ?

Not to begin with, and not if you will taking photos of mostly your art.

I would start with a 50mm lens, this is almost equivalent to the human eye and a good length to get used to when you are starting out.

I've never used too many filters except UV filters just to protect my lenses.

Noted ... You've been a great help.

If you have any more questions feel free to ask!