Your question is not easy to answer as there are several H-bridge configurations. Also, H-bridges are simple in principle but not so much in practice. Do you have a schematic of the H-bridge you wish to build? This would be helpful for us to suggest parts.
As to which MOSFETs to use. Yes, there are many to chose from. Since they will be used basically as switches look for ones with a low Rdson (the resistance between the drain and source when the MOSFET is fully turned on). Then the Vdss (voltage between drain and source at saturation) which should be a couple times the voltage used (50V minimum for a 24V supply). The Id is the drain current and should be greater than the motors stall current. Finally the Vgs which is the gate to source voltage to fully turn on the MOSFET.
Power MOSFETs have a good amount of gate capacitance and may require lots of current to turn on the gate. So a MOSFET gate driver may be required, this can be a chip made for this purpose or a bi-polar transistor or a smaller Mosfet. Therefore a logic level gate is a mote point and the Mosfet with a higher Vgs is fine.
Lastly is the MOSFET's power dissipation or how much heat can be removed. The Rdson is part of this, from Ohms laws and the power equations Mosfets with a very low Rdson don't dissipation much heat IF they are switched full on but when switching on/off at PWM speeds they dissipation much more heat. So look for a mosfet package that can be heat sunk like TO-220s (these are leaded parts that are easier to use by a hobbyist).
I tried to explain the hows and whys of MOSFET selection. I looked at the H Bridge tutorial but could not find the Mosfet part number on-line that is written in the tutorial. Also the tutorial is to show the basics of how on H-bridge works and has a few issues in practice. Here is a better circuit:http://www.cadvision.com/blanchas/hexfet/np-s.htm
The Digi-Key PNs for the Mosfets are: IRF9Z30PBF-ND & IRFZ40PBF-ND and will work for the motors and voltage you chose.
Do be prepared to burn up a few parts, I did when learning how to build H-bridges. When some thing burns up analyze what was wrong and fix it before doing it again. When it all works though it is a great satisfaction to have built it yourself.
Another way is to use one of the many Dual H-bridge chips. These have all the extra stuff inside making them very easy to use.
Good luck, have fun and come back here to ask more questions.