carbon road bike wheels is designed to have either clincher
If you just want a good set of racing wheels and can afford it then go for carbon ones.
So the bottom line is, spend as much as you can on wheels!
Tyres
Good quality tyres are a worthwhile investment. Better quality material gives you longer lasting tyres that are more puncture resistant and lighter than lower quality tyres.
carbon road bike wheels is designed to have either clincher or tubular ('tubs') tyres. You can't change from clincher to tubs without changing the wheel. It is possible to change the rim of the wheel to enable you to change tyres but this is complicated and if you want to do this speak to a bike shop!
Clinchers are the most conventional tyres. They have a bead that hooks onto the rim of the wheel, with an inner tube inside.
Tubulars has an inner tube that is sewn into the tyre and then glued to the rim of the wheel. So you don't have a separate inner tube and tyre.
Once upon a time tubs were faster because they were lighter and better quality than wheel accessories clinchers. However advances in clinchers over the last 10 years means that there is now no real difference between the two types.