Okay dokes. Lets see what I can begin with because there is ultimately a lot being asked here.
Equipment may be an easy one. A good soldering iron is a must. This is usually one that is temperature controlled, has changeable tips and is normally in a "station" like setup. This will likely be more expensive than the pen type ones that you just plug into the wall and go but you'll realise pretty soon that soldering with them becomes quite messy as the solder and the component you are soldering don't heat to the right temperatures. I would start right with that and get practicing by getting some off cuts of wire and soldering some joints on a small piece of veroboard or other copper holed surface to get an idea on how to solder correctly as this is a good way to reduce errors due to bad joints, which I can say from experience, is a very hard thing to debug.
http://www.beavisaudio.com/techpages/How-to-solder/
Which leads me to my next point. Multimeter. Get one. It'll save your ass in so many situations. Forget how to check resistor colour bands? It'll have you covered. Need to know the pedal current draw? Check. Need to see if two points have continuity or not? Yep. HFe of transistors? With some multimeters, yeah, you're golden. Awesome tool, keep it by your side and it'll save you many headaches. Other equipment is simply stuff like solder (60/40), desolder braid, pliers, yada yada yada. Consumables.
If you want to start off with a kit (fully support that), try somewhere like Small Bear Electronics and look through the list of kits/projects. There are a number of projects there that will help you get familiar with the building side of things and severely reduce the stress of ordering the right parts and forgetting something

. Typically, easy builds will have low component parts and less complex wiring. Fuzzes are usually a fantastic example although when it comes to modding, a random knob/pot appears, then another... then another. It grows. Anywho, look at the kits in the link below for a start.
https://www.smallbearelec.com/Projects/ProjandProd.html
So lets say you've ordered and made a kit or two. If done right and debugged properly, it'll sound great and you won't want to kick it off your pedal board any time soon. Awesome. Next thing I would recommend is getting some reading done. Geofex. There is a whole wealth of information there that goes into a lot of depth about how particular aspects of each circuit work and why they do/don't. This is also a great site if you want to think of ways to mod circuits once you realise what part of a circuit does what.
http://www.geofex.com/
Basically, at this point, I'd go buy a decently (not overly expensive) soldering iron station. Get a kit from the link above or something similar which will reduce the project to just building and see where you get to from there. If you can complete a kit, fantastic. You may find that you didn't get too into it or you got completely suckered in like me and can't help working on pedals.
