Nice
Looks like you're doing it proper. Always a relief when you pull the barrels and the nikasil is good
Tyre wise there are a few options.
Bridgestone BT090's have been around forever and offer good grip and and life. Used them on my track bikes and have been happy with them. These are the cheapest as well.
If you want something more modern then you can gp to the best(?) tyre, Pirelli Supercorsas which supposedly offers the best grip but also very expensive.
There are Bridgestone RS10's which are also more modern and compete with the supercorsas but not as pricey.
Lastly there are Dunlop Alpha 13's which have a dual compound (harder in the middle). They are in between supercorsas and Bridgestones price wise I think. (I read somewhere they have now been replaced by Alpha 14's?)
All these come in the correct size (110/150) and are H rated.
By the way, that old rear tyre of yours looks like it would have provided a confidence inspiring ride