I bought a new Craftsman from Sears a few years ago after my used one kicked the bucket. It was under $200, push, bag, mulch, just like your wanting. Big wheels in the rear and small up front. Prob had it for about 5 years now and no problems. I use 100% gas, don't winterize it, keep it in the shed, washed it once, starts everytime. I'll see if I can find a link but the price may be different now.
Same experience here. Had good luck with two Craftsman push mowers.