Advice on choosing Servos and Power Supply

So I'm looking into making a robot kind of like the one featured here: Autonomous-Webserved-Tanktrack-Robot by donboy - Thingiverse. It would vary a bit as I want to try building some of the pieces out of knex instead, and the problem I'm running into is I'm not too sure which type of servo I would need for this project.

(I looked at the one linked and the problem I'm faced with is I live in the US, the hobbycraft servo that is rather cheap is made in the UK (man those prices make me wish I lived in the UK a bit))

I have some specific applications planned for the robot, one being I want to add a depth sensor and see if I can get it to automate making a map of the room it is in. I know for this I will need some precision on the servos for the tracks, but I don't know how accurate something like that would actually get to be.

I've looked at a couple different servos, and this is the one I was thinking might be a good match for the project:

(I was going with metal gears to hopefully make it last a bit longer, also I know it's a bit bigger, but the added size could help with the knex pieces making it a bit larger and if I ever want to take it apart for a different application)

The second problem I'm running across is that I don't know much about selecting a good power supply / battery.

The listing says the current usage is 3Amps on the servos, but that seems a bit high, so I'm guessing that would be for the initial startup (unless I'm wrong, I'm very new to this so feel free to correct me).

Basically if anyone has any recommendations on good parts (or if they happen to know the parts I selected would / would not work) it would be very much appreciated if they let me know. I'm trying to budget around $60 for a good power supply / battery (including a way to charge it) and $40 for the servos. If that's too low I could start out by making just the wheels and come back to the arm later. An explanation for why you chose the piece would be awesome if you could provide that as well.

I'm going to be using an Arduino attached to a Raspberry Pi Zero to control the robot, and plan on adding an infared communication device (KY-022 Infrared Receiver Module - ArduinoModulesInfo) for sending remote communications. I want to keep the laser pointer and camera for later on, and I'm hoping to get a decent hour or two of battery life.

$40 for servos? forget it. You need robotic servos with metal gears and 2 bearings for the actuator, all others will die within minutes. On the wheels you can use cheap standard servos - you'll have to modify the electronoics anyway.