I really wouldn't recommend going 18650s unless you already have access to a spot welder and know what you're dealing with there (would treat the battery build as a separate project really it's a lot of work to do a battery build properly). There's a ton of discussion about it here:
https://www.electric-skateboard.builders/t/please-review-my-battery-pack-so-i-dont-make-a/70102/51
In the case of a quad you don't have as much to deal with as the esk8 with regard to power draw or vibration but still a lot of good advice on that thread if you do decide to pursue that.
With regard to weight this is a huge issue. The lift is dictated by how fast the props can be spun how much surface area their diameter makes up, pitch, etc. etc. there are a lot of variables. This is the most comprehensive calc I've seen for getting some realistic numbers on everything for from scratch builds:
get your electric rc drive right ✓ fast & reliable simulation - no more guessing ✓ most comprehensive motor database ☆ prevents mispurchase since 2004
ecalc.ch
For 5" props a 250mm-300mm frame is usually appropriate (I have a 226mm frame with 5" props they are very close to the frame but it does work fine and smaller size means rotational speed can be higher).
Generally I fly with 4S batteries (1300mAh or 1550mAh) and 2600kv motors, think this is a pretty typical setup now but there are also people playing with lower kv motors and higher voltage (6S) since that means less amperage and less loss through heat and less sag since the amps are split across more cells so guess just more consistent if Wh are equivalent.
Regarding video having receiver goggles with diversity antenna and/or just a good receiver makes a big difference in range you can expect to get. I've generally used AKK's VTX(s) and have worked pretty well for me. Personally running a runcam split 2 since it does HD to an SD card and transmits the lower res signal to the VTX for live view in the goggles and I prefer not having extra gopro weight on there (gopro does have "superview" and generally better looking video, but trade off)