I’ve got 3/64 in my supply drawer. So 1/16 should be OK. You might want to get a piece or two of 3/32 too just to have. I have some of that as well but don’t use it as often.
I get my shrink tubing at allelectronics.com. I bought a 100’ role of the size I use the most 3/16". They also have an assortment with several sizes which I might pick up too. I don’t like the assortment from Radio Shack.
I usually buy the assortment packs of the smaller sizes. 1/16 and 3/32 get used up the most. If you are neat with your connections, it doesn’t take a huge piece of shrink tube to fully cover up.
I picked up two cases of these from Menard’s. Comes in snap-lock plastic case. Six different sizes, starting at 1/16 which you get 60x3’’ inch lengths and up to 3/8 tubing:
Larger sizes are great for power transformer wires in control panel, repaired lamp cords, extension cords, many item’s around everyday households, garages etc., unless of course, You don’t do that kind of work. LOL They eliminate the need for electrical tape in many applications.
If there is a little space, I cut a piece of Vero PC board for soldering wires together.
I have a heat gun. Some use a hair dryer with a tapered tube to concentrate heat into a narrow stream. Some use a soldering iron with small tip but watch out for any plastic.