Would you please indicate a good family of FETs/IGBT's for this matter?
Any FET's with at least 3x the voltage and current will work perfectly. With your particular setup though, I would change that to ~3x the voltage and over 4x the current, FET's with those numbers are quite easy to get and cheap.
Can't go wrong with any of these.
DigiKey
https://www.digikey.com/product-detail/en/AOT430/785-1145-5-ND/1855917
https://www.digikey.com/product-detail/en/STP60NF10/1026-STP60NF10-CHP/2521385
https://www.digikey.com/product-detail/en/AOT460/785-1146-5-ND/1855918
https://www.digikey.com/product-detail/en/STP80NF12/1026-STP80NF12-CHP/2521390
Mouser
https://www.mouser.com/ProductDetail/ON-Semiconductor/NTD5862N-1G/?qs=sGAEpiMZZMshyDBzk1%2fWiy8mkjihaa%252bLsHrwImjMh9Q%3d
https://www.mouser.com/ProductDetail/Infineon-Technologies/IPP057N06N3-G/?qs=sGAEpiMZZMshyDBzk1%2fWi4GEWCr0KJSE3GE5sBsT8kU%3d
https://www.mouser.com/ProductDetail/NXP-Semiconductors/BUK7513-75B127/?qs=sGAEpiMZZMshyDBzk1%2fWi9tVkC2LaBCdc%2fetkdhgQ2c%3d
https://www.mouser.com/ProductDetail/NXP-Semiconductors/PSMN016-100PS127/?qs=sGAEpiMZZMshyDBzk1%2fWiwlkuHBjkY0VWW8NYwLE1Xk%3d
There is a problem here though, all these are N-FET's, most H-bridges use P-Channel for the top side switches, generally so the control can be shared with the bottom side switches. This CAN be avoided, but requires some extensive ingenuity. The best I have seen was someone using opto-isolators in a clever configuration. If you know how to do this or similar, great, I highly recommend it as it lets you use cheaper parts that are actually better. Plus you get to use one part for all four switches, which lets you potentially gain bulk purchase discounts. In any case, here are some P-Channel units if you want to make a "conventional" H-Bridge. Which should be far easier to design and build.
DigiKey
https://www.digikey.com/product-detail/en/SPP80P06P%20H/SPP80P06P%20H-ND/2081673
https://www.digikey.com/product-detail/en/IXTP96P085T/IXTP96P085T-ND/1995412
https://www.digikey.com/product-detail/en/IXTP52P10P/IXTP52P10P-ND/1995407
https://www.digikey.com/product-detail/en/SUP75P05-08-E3/SUP75P05-08-E3CT-ND/3758733
Mouser
https://www.mouser.com/ProductDetail/Infineon-Technologies/SPP80P06P-H/?qs=sGAEpiMZZMshyDBzk1%2fWi5eGkr%252bPRUK3ycad2k5yKXs%3d
https://www.mouser.com/ProductDetail/STMicroelectronics/STP80PF55/?qs=sGAEpiMZZMshyDBzk1%2fWi1qxDdW%2fXBi2hekoN3GjTiE%3d
https://www.mouser.com/ProductDetail/International-Rectifier/AUIRF4905L/?qs=sGAEpiMZZMshyDBzk1%2fWi6rYPvSui93I7R7xZwnh1UY%3d
https://www.mouser.com/ProductDetail/International-Rectifier/IRF4905LPBF/?qs=sGAEpiMZZMshyDBzk1%2fWi5%252bqVgN3%252bWS8xZ2k6vtUc%2fg%3d
Driving sequence
Note that there is a particular way to drive an H-Bridge that is most efficient. I will explain in reference to this diagram...
When you want to drive the motor one way, let's call it forward, you would HOLD switch one(S1) ON, and you would then PWM switch four(S4) for the actual speed control. This gives you one single point that you are turning on and off which makes switching much cleaner and more efficient. Since switch four(S4) is an N-FET, you get the best PWM performance do to it's characteristics. This is because the P-FET's just acts like direction choosing switches, so their high speed switching characteristics don't come into play at all.
Now, if you want to change direction, you would make all the switches off/open, wait for a specified dead time, (or preferably, until the motor has completely stopped), Then you turn on switch three(S3) and PWM switch 2(S2) just like you did before, only this time you're going the other way, or breaking (stopping, not destroying) the motor. If you want to change directions again, you use the exact same process, just with the first switches again.
Note that a PIC ECCP already implements the above logic when set up in Full-bridge mode. All you have to do is decode how to set yours up this way from the data sheet. Otherwise, it's up to your ability to be able to do it in pure software by yourself. It's not really hard, but it's not nearly as convenient as using the ECCP when you have one.
FET Drivers.
Even if you get four logic level FET's, you will need to have some strong drivers to switch them quickly and cleanly. The good news is you really only need this on the bottom side switches, as these are the switches you are PWMing. You are really only using the top side to direct the current, and you only change them infrequently and usually only when the current is already off. So it is enough to use conventional drive strength, or if anything, higher voltage for the top side switches.
If it were me and my design, I would use BJT push-pull buffer that can sink-source at least 1 Amp current. This gives you the strength needed to really get those switches moving, and lets you use a higher voltage for driving the bottom side switch gate. I would drive all the FET's to 10~12 Volts for best performance.
Another option is to get a purpose built IC that goes in-between logic and an FET. This seems to be what all the cool kids are doing these days, you can't go wrong with this. But, you will have to have someone else help you pick one of these IC's out. As I said, I personally would just use BJT's and some such circuitry. But I can do these things.
Current feedback
If you want current feedback to your PIC, to let you so things like calculate motor power or detect short circuit, you will need to insert a current sense resistor between ground and the bottom of the lower switches. This gives you a voltage drop across the resistor that is proportional to the current through it and it's resistance. I would use a low resistance, high wattage resistor, like 0.1 ohms 10 Watts. I would then use an Op-Amp to boost the output voltage up to a point that the PIC's ADC could read it, so to about 2.5 volts. That, or I would use a Schmidt triggered comparator and just implement overcurrent shutdown.