I don't know about doing tickle vids, but I've a bit of knowledge of shooting films, so hopefully I can help witht he first two questions.
Basically, the more money you spend, the better the equipment and thus the end result will be too.
A camera is going to be expensive, so you may want to think about renting, unless you're planning to make this a long term project. But considering that the porn industry really isn't going to make you that much money, especially if you're only focusing on one fetish, then you're better off finding a cheaper alternative (and hence, the renting).
There are too many types of cameras about to go into detail of each of them, so what I say you do is find out what type of cameras are available to you and then research which one is best for you. Personally, I'd go for something like a High Definition camera because the quality is obviously better than a standard definition. You could get a small handycam fairly cheaply, but remember that people will be more interested in a crystal clear image than a really grainy one, and these handycam type cameras don't have the best quality.
After the camera, you're going to need somewhere to edit it. I use a Mac with the program Final Cut Pro on it to edit it. But this is high end stuff. If you have a PC, you can download cheap or even free software that'll do the job. You won't have all the fancy bells and whistles that the pros use, but you'll get by. Just be aware that you have to make sure you have the right connection to hook the camera up to computer. Most cameras would need a firewire slot.
Another thing to consider is a mic. Most cameras will have an in-built mic, but the quality of the sound may not be great. And everytime you touch the camera, every movement you make, and a lot of the time, the noise from outside, will be picked up by the mic. If you could get a seperate mic, it might make the sound much easier and clearer to use when editing.
So that's the equipment, basically. You need something to get the picture, something to get the sound and something to edit it all together.
After that, you need a location. Now I can't tell you where to film, but I can tell you some things to bare in mind.
Firstly, find somewhere quiet. As I said above, your mic will pic up every sound that's made, even things that you can't hear. You pressing a button on the camera can come out as a deafening click, or in a quiet moment, you might be able to hear the neighbours tv.
Secondly, watch your light. You have to keep your film are well lit and you have to watch out for shadows. If the light is above you and you leaned over you lee to tickle them, they might disappear into darkness as your shadow covers them. You can rent lights or maybe just get some lamps. Don't point them at the area you're filming as this creates more shadows. Instead, you diffuse the light, by either pointing the light at a flat white (or near white) surface and the light reflects around the room. This softens the light, so it still illuminates the target, but stops the shadows from being as strong. Another handy trick is to use greaseproof paper over a light. It does the same thing.
Finally (until I can think of anything else), know what you're filming. Have a rough plan of exactly what you want and what shots you want to get. Practice with the camera before you do anything, so you'll get the hang of it and know where it should be and how to make sure you don't block shots etc.
All in all, it's awkward to setup, but filming is always fun 🙂 Hope it goes well.