First of all congrats with your 113!
you need a 1.6 mm flat screwdriver, this is most probably part of the box your watch comes with.
the tubes are like the straps for your watch 24mm, you do not need for every strap a set of tubes, you can swap them between straps.
When it comes to size, you need to figure out what YOU prefer, as some wear straps very long, others very short and dont like the extra tail of the buckle siting on the side of the wrist instead of in the middle of the wrist. My first aftermarket strap I got I ordered it at 135-80, the maker told me to go for a longer strap, I was stubborn and turned out to be wrong, I needed a bit longer strap as the thickness of the strap makes it wear different than a 115/75 Panerai OEM strap size. My next straps I ordered from the same maker was 140/80 that looked already much better and my last one a 160/95 as a real bad-*** long tail strap for my PAM372. Now most of my straps are either 140/80 as dress straps or 150/90 as casual straps.
Micah Dirksen has some good advice on that, you can google his name and you find out what his website is.
As an example my wrist is in the summer 18.5 cm/7.2", I like my vintage straps long with GPF Mod Dep style buckles (flat buckle) and straight, aftermarket straps are in general 24-24 straight straps, the Panerai OEM straps are 24-22 mm, most of them at least. You need to understand that the aftermarket straps are often a lot thicker than the OP OEM straps and therefore your need to add a bit of length to get the same effect on an aftermarket strap that is 5mm, on both sides 5mm extra length.
Personally I like the tapered OEM straps on a 44mm Panerai as the tapering is not that extreme like on a 47mm model with 26-22mm.
You could check out the Accessory Collectors Corner on the forum, there are a lot of strap on sale in different shapes and sizes, this can give you a good idea what is available out there.
If you have any further questions, just let me know!
And do not forget to post your first images of your 113!
Dutchman, Panerista since 2014 and learning
PAM389 and PAM372 and a bunch of straps