I've never used the Shinkos, just the Kenda Challengers because they're cheap and seem to hold up just fine. You have a 79 like me so you'll need to get new tubes with them as well. Just FYI if the tubes have two nuts make sure both nuts are on the OUTSIDE and the dished washer goes on the INSIDE. I actually paid a shop to do tires and tubes on a machine for me a couple of years ago and they left one nut on the inside and it eventually ruined the tube. Luckily I was 2 miles from the house so I just lugged it back home, but just make sure that doesn't happen to you.
I believe the Kenda Challengers are out of stock in most places now, so the Shinkos are one of the only options right now. For sprockets and chain, highly recommend you get a DID natural chain. It's 102 links and there's a couple of vendors on Amazon that have it already cut to length:
https://www.amazon.com/chain-520-Did-102-Links-Standard-Open/dp/B000XY4SYM/. Don't get an O-Ring/X-Ring chain; it's a waste of money and they won't fit these older bikes. Don't get any cheap Amazon sprockets. Instead, Sunstar does have sprockets. They are pricey, but they are worth the expense. For some reason, their rear sprocket has been out of stock for quite some time. Another option is Sprocket Specialists. It's 16 teeth in the Front, 38 teeth in the rear:
https://sprocketspecialists.com/product/front-sprocket/ and
https://sprocketspecialists.com/product/rear-sprocket/.
Front Tube is: 120/80-18 -
https://www.amazon.com/IRC-T20064-Standard-Tube-5-10-18/dp/B00230OFXS
Rear Tube is: 120/90-16 -
https://www.amazon.com/Standard-Motorcycle-Inner-Tube-Kawasaki/dp/B073W2388S
If you must do the tire yourself make sure you get these tire irons, they're cheap and they work fine if you are careful:
https://www.amazon.com/Motion-Pro-Tire-Iron-Piece/dp/B001DDD8E8. I highly recommend you just put the bike on the centerstand and put something under the front forks (like a cinder block with a blanket) so it doesn't fall over and just take the rims to a shop. They'll change the tire quickly and cheaply if you just bring them the rims, tubes, and tires. I only change mine myself in an emergency because it just takes too long without a machine and the chance of tube puncture goes up if you don't have a nice machine to do the work of removing the tire for you.
When you put the rear back on, get the chain aligned to the marks on the swingarm as best you can. Err a bit on the looser side, then snug tighten and check and see what you have. You'll find that most times the chain has tightened a bit. So going a bit looser will compensate for that and get you where you need to be. It's good to check alignment with a straight piece of metal like a long brass rod, but motion pro sells a tool just for this purpose that works well:
https://www.amazon.com/Motion-Pro-08-0048-Chain-Alignment/dp/B000GTVOJQ. Once the chain slack and alignment is correct, spin the rear wheel and lock the rear brake. Then finish the tightening sequence. This will align the rear brakes better to the hub which helps with braking.
Forgot to mention, when you clean the fuse box spray the fuse ends and the their holders with contact cleaner then insert/remove multiple times and spin them around to clean it. Put some dielectric grease on the fuse ends. You just need a thin layer. Put them in the fuse holder and spin them around to distribute the grease. As long as the fuse holder isn't too dirty this should help prevent excessive resistance build up in the fuse box that will leave you stranded. Your bike looks very clean, so most of this should just be preventative maintenance for you.
Another thing to mention, check the oil weekly on the centerstand. Find out how much you lose. These bikes, especially the Hondamatics, are sensitive to low oil. You'll probably be losing some oil. This is normal, especially considering the bikes age with seals and gaskets, but make sure you keep it topped off. Running low on oil with the 400 twins will cause damage. It's not unusual to start putting miles on it and finding the shifter seal and kickstart seal start weeping some oil. You can replace these seals on the bike without having to open the engine if you are careful. Expect the valve cover mounting bolt grommets to start leaking oil at some point since they are old. The valve cover gasket itself may start leaking. If either of them do, get the OEM parts. Don't use RTV, it will ball up and get in the oil supply and ruin the bike.
Fork seals may eventually start leaking after a few months. You can do it yourself, but you will need a vice, a breaker bar, a pry bar or very long flathead screwdriver and the correct allen socket to do it. If you don't want to invest in all those tools, just take the tubes off and buy the seals and bring them to a shop to have them swap them out. Will be cheap if you just bring them the tubes ready to go. I recommend you DON'T use All Balls seals. They're just rebranded cheap Chinese seals. It seems hit or miss if they start leaking or not. You can still get the seals OEM, or take the seal size to a bearing supplier and get something decent. Fork Oil I just Honda SS7 from the dealer, but really you can use any brand of ~10W fork oil and it should work fine.
I know it's a lot of info to take in, but if you do all of these things most of it you really only have to do once. After that it's regular oil changes, valve clearance, chain slack, lubing, and cam chain tension from here on out and you can go many years with no problems.