Choose the sturdiest frame, everything else can be changed. You will wanna buy new rims with 12-guage spokes (that means just buy the wheel with the thickest spokes you see) buy one of those wide seats with the spring suspension, it makes SO MUCH difference to your ride comfort.
Front suspension is nice, too.
I got a cheap Huffie mountain bike, changed everything that wasn't the frame. Only the wheels ever gave me trouble, but that was before I switched them.
If you plan on being able to still pedal, then don't buy a cheapie bike. Their chain drives always break right away, or get out of line, or just fall off.
for me, though. The bikes weight made no difference, it weighs over 100 lb on its own without rider and still gets me past 40 with no trouble, acceleration is awesome and powerful too.
Keep in mind- front suspension precludes adding a basket, UNLESS you reinforce the two legs. Because those legs won't flex with the spring on the suspension, the weakest points are at the bottom where the extra axle holes are drilled.