Typically the front steering neck area of the frame has a sticker that says model + year. I'm not sure how the old ATC70's are, but like a 1979 ATC110, it only has a serial number stamped in it and you have to use a vin decoder to get the correct year. The site I used to use all the time appears to have just went off line. Maybe they are just late on the hosting bill. I guess I'll have to mess around and script up a decoder and throw it up on my site some time.
https://atcvin.webs.com/
Anyway, for advice, I personally like to give any new to me machines (including cars etc) a basic tune up. In the context of an ATC70, that would be a new NGK spark plug, air filter if it doesn't look new, and a fresh oil change. I'd look over the machine and see if you can find excess slop in any of the bearings, mainly steering stem, front wheel bearings, and rear axle bearings. Also check out the chain & sprockets to what their condition is, I'm pretty sure the ATC70 has a tentioner, so you might want to grab a
service manual and adjust it if it doesn't match what the
service manual says. Besides that, get your carb to air box boot and the wire thing you mentioned and have some fun on it.
Here's a place to get
service manuals, based on the year range on the site, the ATC70 was made 73-85, so lots of years, so probably a lot of minor things changed. I don't know the 70's as well as other models, so can't be much of a help with differences year to year.
http://www.oscarmayer.net/atc/manuals/
If you do decide to run the K&N filter, you'd probably have to re-jet the carb to get it running right. Not sure if there's anything special about the 70, but typically the direct filter will make the engine very lean, so you need larger than stock jets. Also if you go that route, a higher performance / free flowing exhaust might balance it out a bit better to match the intake mods. I can't really recommend what brand of exhaust to look for, most of the aftermarket ones are just mega phones that make more noise than anything. I kind of doubt supertrapp made an exhaust for the 70.
Good luck with your build, and we always love photos, so if you can post some, maybe we can notice something else, like aftermarket
parts, or things missing etc.