You will never regret having too much power. As long as you're building this from the ground up consider a 15 Ah LiFePO. Same size factor as that old SLA 7 Ah and easily a third lighter. Check with our sponsor Amped Outdoors. Drop Matt a line before you order and he might toss you a Shanty discount.
I'd also install USB capability to recharge a phone, mini camera, etc. Looked at your Insta and I'd make a couple of changes. First, I would not use those screw post connections. A much better option is an SAE polarized connector. Low profile, always polarity protected, and infinite accessories can be adapted to it. Looks like these:
To mount on your box
To add to your accessories.
You can even em' to attach a charger so you can recharge with out having to open the box or remove the battery or any wiring... All of these electrical goodies are easy to find on Amazin or I can share some links to some of the stuff I've used.
Cordless battery adapter? Ridgid? Not sure what your question is here...