There is no right or wrong.  The pros all use tubulars when they race.  Many use clinchers when training.

The advantages of clincher tires are they are easier to mount and it's easier to fix a flat.  You can easily remove a tube and either patch it or replace it.  You can also get models that cost a lot less than tubular tires.

The disadvantages of clincher tires are they are heavier and don't perform quite as well (although the differences at the very high end are not great - especially now with the introduction of the wider clincher rims.

The advantages of tubular tires are they are lighter (both because the tire needs no bead to hold onto the rim and because the rims are lighter because the need no sidewall to hook the bead) and the side walls flex better.  The flexibility of the sidewall casing is an important factor in rolling resistance because a flexible sidewall will roll over a bump rather than bounce over a bump.  Since the sidewall is stitched around the tube, the materials used can be more flexible.

In the best tubular tires, the tread is applied to a fully stretched casing thereby eliminating all of the stress between the tread and the casing.

The disadvantages of tubular tires are that they need to be glued to the rim - a somewhat tedious process.  However, you can use rim tape that is relatively easy to apply.  The tires are also somewhat expensive and often you need to replace a tire when you get a flat.  However, what many people do when they get a flat is install tire sealant - which will fix the vast majority of flats.

Lastly, removing the glue or tape when putting on a new tire can be a challenge but there are a couple of tricks that can be used to help mitigate it.  Use some heat (hair dryer or heat gun) and the glue will come off easier - or if you have the time, sit the wheel with the bottom in a bucket with some glue remover - let it sit for a day and all the glue will come off - rotate and repeat.

Acetone is frequently used when removing tire glue but DO NOT USE IT AROUND HEAT.  It's extremely flammable - actually explosive (one of the reasons you can bring bottled water through security check points).