LiPo battery packs should be always charged with a balancer. Today you should buy a charger that has a balancer built in. Balancer checks every cell separately during charging so that they all get charged equally. That is very important with LiPo packs, because if one cell gets charged to a voltage over 4.2V it basically swells up and explodes. If you look at LiPo packs you see that in addition to + and - connectors they have extra connectors to monitor each individual cell. With 2S LiPo it is not very critical to always use balancer, but you still should!
Always charge the LiPo in a fireproof LiPo Sack and never leave it charging unsupervised.
I would buy the biggest capacity LiPo that can be put on the car without exceeding the weight limit too much. Bigger capacity LiPo gives you higher overall voltage during the run.
Basically all ESC-s that support 6-cell work with LiPo. But LiPo has over the 5-minute run higher average voltage and probably gives out more amps also. So you will get more power to the engine which can mean that the ESC heats more. So if you are running the ESC on its limit be carefull and maybe use some extra cooling.
Another important thing with LiPos is that you should NEVER go below 3.0 - 3.2V per cell (6.0 - 6.4V for 2S pack). If you do it there will be some irreversible chemistry inside the LiPo and it will perform worse or be ruined for good. New ESCs have built in LiPo cutoff, but I don't have it on my ESC and if I run 5-minute then I take only 30% out of the battery so I'm safe. I can run 10 minutes without going close to the critical voltage.
I'm running LiPo + brushed at the moment. I wouldn't consider running NiMH ever again. If you have everything needed to run brushed motors then continue doing it with LiPo. I'm running brushed until the end of this year because its faster than brushless that's allowed by our rules
I think both LiPo and brushless give you more trust in your car/equipment. LiPo doesn't run out and brushless doesn't need so much care and maintenance.