Indeed, you cut the existing plugs off and simply solder your choice in place with female on the battery and male on the ESC. Pick a high current connector that you like. I guess you have an advantage not already being invested in one connector, I have to say through laziness, I can't be arsed to reissue my fleet (currently Deans) and all my batts with another plug, so I continue using Deans, which actually aren't sufficiently rated for some of the more heavy duty stuff I do, they are however, still the most commonly used esc/battery connector in RC. If in doubt, just go Deans, they are more than adequate for what you want to do.
More kv means a higher top speed at the expense of a little torque, more current drain from the battery, resulting in less runtime and more heat. The thing to do is strike a balance between kv, the weight of the car and the gearing. On road cars are light by nature and have small diameter wheels, so are not too demanding on their motors, therefore, we can afford to use a higher kv motor before we start generating excessive heat. Worth mentioning I suppose that kv is a direct relation to the number of unloaded rpms the motor should turn, per volt of juice supplied. So, for your kind of car, for general running around, my experience tells me to recommend something around 6000kv for a good mix of speed and gearing choice. You will then play with gearing according to your needs, while keeping an eye on the temperature of the electrics after making changes. If the motor is getting too hot, you lose teeth off the pinion gear to reduce top speed and initial startup load. If you are seeing low temps from the motor during running and want to have a higher top speed, you can gear up appropriately, making sure not to start running too hot. A brushless motor should not get over 190*F according to my reading (and this is what I stick to) as the resin that holds the whole deal together internally starts to disintegrate after that.
Which speed control...I think they're the exact same thing, being marketed slightly differently, one has an LCD programming card, the other has a standard led/digit interface. Of course the LCD is nice, but not at all needed (as far as I know, it does not give access to extra features, though it is possible that it could). It's up to you. In any case, you are looking for a motor and esc combo around the 6000kv mark, the amp rating on the esc, the higher the better, but don't let that worry you as long as it's over, say 40A, as long as you stick to 2S batteries. Programming devices are WELL worth having, they allow you to change features of the ESC, such as braking strength for example, or put it in competition mode for racing (no reverse
Hope all that makes sense, typed it a bt quick lol.