Building a Rope Kit
Diameter
Almost any size rope can be used for bondage with enough creativity and care; however for the techniques covered in the Core Rope Curriculum, you generally want a diameter between 3/16" and 3/8" (5-8mm). The right diameter depends on the material of your rope and your style of tying more than on the size of your bottom, although wider rope can sometimes be more convenient for tying larger bodies. A good starting point for beginners is almost always 1/4" (6mm), and that's the most popular diameter in general.
Construction
Some ropes have an outer braided sheath around a core of straight fiber; most rope made for climbing is of this type of construction (sometimes called "kernmantle"). Clothesline and other cheap hardware-store ropes frequently also have a core, sometimes of a different material than the sheath. In general, any rope with a core is bad for bondage; it is difficult to handle and produces bulky knots.
Rope for bondage should be either twisted (most commonly with 3, but sometimes 4, strands), or a solid braid with no core.
Color
When you are first starting out, it is best to avoid black rope or other very dark colors; it is harder to see what is going on with dark rope, both for you and for your teacher if you are taking classes.
Length
It's sometimes joked that bondage ropes come in only two sizes-- too long, and too short. I recommend keeping some of each handy.
The main consideration in choosing the length of your ropes is how long a rope you can comfortably handle without it becoming unwieldy when you're pulling it through. This depends mostly on your arm span, and in part on your style of tying. I'm 5'9" and find anything longer than 27' to start becoming awkward for me.
My recommendation is to compose your kit primarily of the longest length that is comfortable for you to work with, and then add in a few shorter ones for when you just need a bit of extra to finish up a tie. The most common lengths offered by suppliers of finished bondage rope are 25', 8m (26'), and 30'. My approach to building a kit from retail bondage rope is to buy 10 of the length they offer closest to my ideal (usually 8m), take one of them and cut it in half, and another cut about 1/4 way down. That gives me a kit of 8x full length, 1x 3/4 length, 2x 1/2 length, and 1x 1/4 length. For a smaller kit, just decrease the number of full-length ropes.
When you are just starting out, or if you are doing mostly bedroom bondage, a smaller kit with a higher proportion of short ropes may be more convenient; I find in the bedroom I rarely use more than 5 ropes, and use each of full, 3/4, and 1/2 length ropes with about equal frequency.
Cutting a couple of ropes to make yourself shorter lengths is a good opportunity to test that your safety cutters work well on the rope you're using. You'll need to learn a method for finishing the rope ends, to keep them from unraveling.
Material
There is another article dedicated to rope materials. If you are just starting out and don't know what you like yet, I recommend looking for inexpensive but high-quality 3-strand cotton or nylon. I link to my favorite supplier for cotton rope here.
Stuff to Carry Other Than Rope
There's a variety of items other than rope that you may want to keep in your rope bag. Surely the most important is safety cutters, but beyond that here are some to consider:
The most common rope-kit first aid supply is ibuprofen, which is traditionally recommended to be taken immediately after a wide variety of the injuries most likely to occur in rope (nerve compression, pulled muscles, joint injuries) -- however the science is pretty mixed on whether that actually promotes healing or just makes people feel better, and you should always be careful that taking pain relievers doesn't encourage you to ignore pain that should be listened to. Similar story with cold packs, which should almost certainly not be used in case of nerve injury but might be helpful with joint injuries.
Having a sugary snack and water immediately available is always a good idea during play. Flashlights can be important in an emergency (although most cellphones can fill this need in a pinch). Simple first aid supplies for cuts and scrapes are good to have, although the risk of those isn't really particular to rope. Some tops like to have a hand balm with them; tying a lot can be murder on your fingers.
If you've got space in your bag, a thin cloth to lay over the floor where you'll tie is nice to have if in a venue that doesn't provide clean mats. Alternately, a blanket serves the same purpose as well as being a great aftercare item.
When tying someone who may need emergency medication (e.g. inhaler, epipen), always make sure they've got it with them and you know where it is and how and when to help them use it. For a while I dated someone allergic to bees and we tied outside a fair amount, so I kept her spare epipen in my rope bag.
Got other stuff you like to carry when playing with rope? Let us know in the comments.