Depending on your rim (bore diameter) you don't have the choice unless you are willing to tweak your bike a bit (or use an adapter). Cross-Country or Marathon Hardtails and racing bicycles usually use Presta aka Sclaverand or French Valve (at least we call it like that in Germany). This type of valve opens when you put the pump on it (after you opened the screw). This allows for measuring the pressure but unfortunately it can be really annoying because you normally release some air when trying to set the pump correctly. Still, Presta allows for a pressure up to 15bar. This is required by racing bicycles. A disadvantage is the thin and long shaft which makes it more likely to bend the valve unwanted. Still this can be an advantage because this more elegant design reduces weight and therefore dynamic unbalance.
Schrader only allows up to 10bar pressure. Because the valve opens mechanically, we can measure the air pressure just like for Presta. The risk of loosing air/pressure at the beginning is lower because you first set the pump on the valve and just afterwards open the valve with a lever.
The biggest advantage of Schrader is that you can use pumps at gas stations without an adapter. Those adapters are really cheap and small, I always carry one in my purse between the change. But still you don't have the risk to loose that adapter when you are using Schrader valves.
The biggest disadvantage of Schrader is the relatively small pressure you are able to establish using hand pumps due to the bigger cross sectional area (p=F/A). Because of the differences in the mechanical construction and therefore the sealing, also with automatic pumps you can't achieve the big pressures compared to tires with Presta valves.
As you can see both valves have their pros and cons. Simplified, If you have
- thin rims and/or
- don't want to disturb the stability of the rim and the dynamics of the tire and/or
- need big tire pressure and
- don't care about the issues of maintenance
you should use Presta. For all other cases, use Schrader.
By the way there are more than two types of valves used for bicycles but I think the two mentioned are widest spread