If you need tyres for riding on the road, then get ones with a minimal tread, not with knobbles. Smoothe tyres roll more efficiciently and are more fun on the road.
With your 3x7 gearing system, you should try and avoid combinations which stress the chain sideways, ie small chainring and small rear cog, or large chainring and large rear cog. There are plenty of duplicate ratios in this system, so there is no need for cross-chain combos. Its hard to asses a gearing problem without inspection, so take it to a good local bike shop.