Charger: I'd recommend the
Kinexis KX 80 or the
HiTec X1 Mini. I have the HiTEc model (I actually have three HiTec chargers- the older X1 AC Plus and newer RDX-1). Both chargers offer a similar feature set at the same price. While you don't need LiPo (or other chemistries) at this point, I'll wager that you'll move to improved power systems soon enough and having that capability will be good- you won't have to buy another charger. Kinexis is a Horizon Hobby brand and they offer famously good customer support. Hitec service is also very good.
Battery: I recommend getting another Dynamite Speedpack. The "mAh" (mili-Amp/hour) refers to the capacity or run time of the battery. The larger the number, the greater the capacity and thus longer the run time. 1800 mAh that came with the car is pretty wimpy. The 4500mAh pack will give you 2-3 times the runtime of the stock battery.
Tools: Most of the fasteners on the stock ECX cars are Philips. I'll bet you have one of those laying around. There are a few screws that are hex so I'd suggest you get 1.5mm, 2mm, 2.5mm hex drivers. You can find Dynamite and Kinexis "starter sets" that look attractive but I've found that the bits are too soft and round easily.
This set (DYN2904), with the three sizes I mentioned above, is nice and not terribly expensive. I've been using my set for over a year now with no complaints. There is also
this set (DYN2030) that includes a 3mm driver (but I rarely use 3mm fasteners on ANY of my five cars!). All the bits are replaceable in these tools.
As for extra parts? Hard to say. ECX cars are generally very tough. The front end on any car tends to take the brunt of crashes so I'd recommend that you install a
T-Bone bumper. I put one on my AMP/Circuit truck and have crashed the heck out of it, both in the back yard and on the race track (crashing into walls, wooden jumps, etc), and have not yet broken any front end component.
The below is assuming that you have a 2WD Torment:
Front swing arms:
ECX1018
Suspension mount set:
ECX2006
I would say that would really be the only parts that you might want to keep on-hand as it's the front end that usually takes a beating. You can stock more but it's always a bit of a gamble. I have parts that I've stocked up on that I have not yet had a need for a year and a half later! So that's money tied up in parts.

Ordering stuff directly from Horizon Hobby usually ships out pretty quickly and with standard shipping you can get orders in about a week.
Welcome to the hobby!