Regards the TX and RX you'll more than likely need to use the same manufacturer as the transmission protocol can differ between them, even if using the same crystal.
You can mix and match motors and ESC no problem, I'm using a Corally ESC and LRP motor. Definitely stick with sensored though as they're much smoother and have more in the way of adjustment, like punch, boost and turbo.
Chargers - again a massively varying budget but at the skinny end I used to use an IMAX B6+ clone - Around £25 new off ebay. Does everything you need, and being the + model has both AC and DC inputs for home and field use. Still have it in my pit box as a spare. I now use a Radient Duplex which can charge 2 packs at the same time, was £60 new. Again don't be put off by 2nd hand stuff, some good deals out there.
Lipos are great but need a bit of respect - don't leave them fully charged or flat, they need to be left in "storage" when done with them - the charger will do this for you. Plenty of useful info out there for a bit of bedtime reading, or just ask on here if you're stuck.
