So I checked with them and they said the kits have a 14mm diameter axle, which coincidentally is exactly the same as my existing axle so it should work without any modifications.
If your existing axle is 14mm, then that means the axle flats on a hubmotor (which are almost always 10mm apart) will just spin inside your dropouts unless you make torque plates or pinching dropout plates, etc., to bolt or weld to your frame.
The hubmotor axle diameter (it's round part) isn't what matters in relation to your existing droputs, it is the distance between the two flat sides of the axle.
That flat part must be very securely clamped in place, as any rotation/movement at all will eventually damage either the securing mechanism or the axle enough to allow it to just spin in place when accelerating or braking, instead of the wheel doing this, and rip your wires up, shorting out the motor, controller, etc. (usually destroying the controller and often the motor halls and anything else that was connected to the controller's 5v (throttle, etc).
The axle shoulder width also matters--this needs to match the distance between the inboard faces of the dropouts, between the two halves of the swingarm. If it's too wide it won't fit in your swingarm. If it's too narrow you won't have enough axle length to secure into the swingarm's dropouts.
My only question at this point is which motor to get. You can see
here that they have 3 motors options. 48/52v 1500w, 48/52v 2000w, and 60v 2000w. I've been trying to figure out what the difference between those would be and my best understanding is that a higher wattage will give more speed and power at the cost of using more energy, while a higher voltage will give more speed but less power?
It doesn't work quite like that.
Watts = power.
Power (watts) = Volts x Amps.
More volts for the same amps is still more power.
More amps for the same volts is still more power.
More Volts (voltage) *generally* = more speed, but *only* if the motor winding (kV, Rpm/Volt) and wheel/tire diameter and current are the same between two different-voltage-options.
More Amps (current) *generally* = more torque, but *only* if the motor winding (kT, Torque/Amp) and wheel/tire diameter and voltage are the same between two different-current-options.
Reality is more complicated, and exactly what you get depends on the actual riding conditions and the speed you're going, so to see how this works, experiment with the motor simulator over at ebikes.ca.
Whether you can even use the more power or more current or more volts in a particular system or set of conditions depends on those conditions and the stuff (electric and mechanical) you've got and how it's configured.
Please correct me if I'm wrong, and which one of those 3 do you think would be the best option? Again, this will just be for casual running around, doesn't need to go very fast or carry much weight.
I can't really guess which would do what you want. Phrases like "Very fast" and "much weight" are highly variable depending on the person talking, and we don't know what that means to you. To me, not going very fast means say, 5-10mph. Not carrying much weight to me means only a few hundred pounds, including the trike or bike, me, and the dog or cargo. (fast would be >20mph, and a lot of weight would be >1000lbs, with several hundred pounds of cargo).
If you don't want define the job you need it to do, and use one of the simulators to at least guesstimate how much power you *actually need* to do the job you need the bike to do for you, then you are better off going for the highest power you can get, so you aren't at least totally disappointed in performance. It might be enough power, or it might not.
Don't forget you'll need a battery that can do more than what the system will ever ask of it, because it will age and be less capable as it does so (the cheaper the battery, the lower quality it probably is, and the faster that aging is likely to happen). So starting out with one that's better than you need means it can still do what you want for some time. The battery is the heart of the whole system, so if it can't do what you need it to, the system definitely can't.
Even better, starting out with one that's even more capable than that by some large margin means it might still be usable with a higher power system if it turns out that whatever you get now doesn't do the job you need, so you're not having to buy *everything* twice (just the controller/motor).