It helps if you look at how the paper travels through the printer. If it curves around before coming out, thicker paper can be a problem as it will jam up the printer. A printer of whatever brand will print heavier pages more easily if the paper goes straight through the machine. Just look where paper is loaded and where it exits the printer. One should not be above the other, but behind or across from the other.
As for brand, they're all pretty cheap so do a little online research for those reccomended. Epson, Brother, HP, all have their fans. Ink prices will be your major cost, so maybe look for a printer that allows longer use of ink or which offers refillable cartridges.
I go to a few stores, write down brand names and model numbers, then look up reviews online. Buying from
Amazon also offers consumer (buyer) reviews which can be helpful.