"If you want to stay with 7 speed, you will need to stay with a 7 speed hub and have it laced to the rim of your choice with good spokes. Then you can move your existing cassette over."
The above is not entirely true and would limit your options. If you have a 7 speed cassette you can use it on an 8 speed hub by using a spacer. Alternatively you can use an 8 speed cassette and set your derailleur up so that it only shifts onto 7 of the gears, the gear spacing is the same. Good 7 speed hubs are hard to come by as 8/9 speed have been the standard for years. If you have a thread on 7 speed freewheel instead of a cassette just chuck it. Freewheels/cassettes are a one of the parts of a bike that is subject to the most wear and they should be changed frequently, do not buy a hub or wheelset for the express purpose of re-using a disposable part.
Higher tire pressure will reduce flats in most cases. A good rim strip will only help if you can pin point that the hole in the tube is on the inside. All that is needed is something with no sharp edges that effectively covers the ends of the spokes.