Well I guess I'm as qualified to answer as anyone

(I started lessons when I was 10 or 11 I think and have been playing now for around 15 years. Ive taught a few pupils over the years and played in a few bands)
A few things to start 'thinking' about before you actually start lessons:
1) listen to the music and try and determine what sound relates to what instruments on the kit- probably easier to listen to fairly simple music drumming wise. This will help you play by ear which is a large part of drumming
2) Start tapping in time (if you don't already) and try breaking things down into 1/4s and 1/8s etc (i.e. left hand taps in time four times per bar, right hand two per bar) Drumming (well, at least most rock drumming) is simply dividing bars up into ever smaller pieces 1/2,1/4,1/8,1/16- and then cutting out notes to arrive at a some thing a bit more interesting)
Then when it comes to actually start teaching, it is good to know your gear: What part is called what and what sound it makes. There are things online im sure to help with this
I then usually start by giving the student one hand/part at a time (similar to chopper flying I guess) and play along while they keep time. Then introduce two elements (say hi hat and snare or hihat and bass) and then let them have a go putting it all together. I find it works better to not *think* about the beat too much.....get one thing going (hi hat) set it in your mind and then put it another part of your mind so you can concentrate on the other hand. Do the same with that and then introduce the next part. I personally try to not focus on the numbers (i.e. teaching beats by counts) unless someone struggles with the 'sound' approach.
Most people have a decent 4/4 single kick rock beat going after one lesson.
I would suggest going to at least a few initial lessons because there are things that cant really be taught without contact and feedback- I.e. how to hold the stick, how to hit the drum, how to let the drum breath etc.
Kit wise: A decent second hand kit is a good choice. Stick with a well known brand like Pearl (although I feel they are a bit overpriced for what they offer), Tama, Yamaha etc....although for the most part the first year or so is probably just going to sound like noise anyway haha. If sound is an issue you can get practice rubber pads which sit over the kit and muffle everything. I wouldnt suggest playing with these too much though as you need to get used to the feel of the drums. I would suggest staying away from electronic kits (initially) for the same reason.
Any other questions, fire away!