This got a bit long-winded....
Wire size depends on the size of the current (in AMPS) and the length of the wire. There are many charts on the web that give similar info. I have used this one but others work as well:
https://www.bluesea.com/resources/1437
You can find or calculate the current draw (in amps) of the lights on the light itself or the packaging. If they are 25 watt lights, the current in amps is (25 watts / 12 volts =) 2 amps or 4 amps for 2 lights. Essentially, 16 gauge wire will should cover your needs but you may need a thicker gauge if your runs are long. Sometimes it's just cheaper to buy on big roll of 14 or 16 gauge instead of smaller pieces of 14, 16 and 22 gauge for each wire run you need to make.
Calculate your fuse size to protect the wire. Since these lights will use a total of 4-5 amps, you could fuse with a 7.5 or 10 amp fuse. Try the 7.5 first. If it blows when you use the lights, check for shorts and then maybe try a 10. Fuses should be mounted as close to the power supply as possible.
As for wire to wire connections, there are numerous threads on just this forum that debate this endlessly. Some like well crimped connectors (especially useful when connecting to the relays and switches) while others like to solder. Others do both (crimp and then solder a wire to a connector). I've used both methods -- mostly soldering only when splicing 3 wires together -- with success. You could use Deutsch connectors but it can be a pain to find the other half (Amazon carries them) or connect to raw wire. You will still have to do some soldering or crimping to make the other side of the Deutsch connector. Use heat shrink to seal the connections if you aren't using something like a Deutsch connector. I like the crimp connectors that have the heat shrink wrap included. There are plenty of videos on YouTube that provide good examples of splicing/crimping/soldering.
For your last question, your vehicle's body serves as the ground. Just ground your lights to the body. On newer Jeeps, it's easy to find various threaded studs attached to the metal body where Jeep grounds various components. Everything on a car works this way. Ground the relay near its location and the lights near where they are mounted. Any connection to the body should work including attaching to bolts used to mount the lights if they are ultimately connected to the body. You can always check a potential grounding location with a continuity tester on a multi-meter or a basic 12v test light.