What GSM of paper should I use for reprinting cards to use in deck sleeves
Paper is a bit more complex than just the GSM as you can get different thickness, stiffness and other properties.

The general "best" GSM for cards will be around 300GSM, but you'll want to feel the sheet of paper first for thickness and stiffness as well. It'll be no good to have a lovely printed card that flops about in your hand or flexes too much to shuffle easily.

This thread on BGG suggests using paper stock that's designed for business card usage as it's widely available. 

This custom card printer uses 300, 310 or 270GSM for their playing cards depending on paper type and required quality. 

You will find a lot of home printers won't be able to print on high GSM paper - check your specifications for your printer if you want to print at home.

If you're getting it professionally printed at a print shop, ask for some paper samples, and have a test page to print on each paper so you can see the differences. 

I had some success in printing at home some card dividers on 180GSM matte photo paper and laminating the entire page in high quality 125 micron before cutting out using a paper guillotine. This produced a very stiff card that was slightly glossy, despite the stock being not that stiff to begin with. As you're planning on sleeving, I'd go the higher GSM paper straight away and skip laminating.