Hello, I'm new to the forum, so this is my first post. I just have a question about installing a new floor in my bathroom.
First I have to mention that I'm not the most handy guy, so if my descriptions or explainations about my situation aren't the best, bear with me

I am also someone who has a disability, so in doing this project myself I'm looking for what would be the easiest option for me to do, which still produces good results.
Currently my bathroom floor consists of what I think are low grade peel and stick tiles. I want to replace it because the floor just looks old, dingy, and disgusting. One tile has lifted and bent at a corner, exposing whatever it was adhered to underneath. Other tiles have slight seperations between them, and others have edges that are riding up onto adjacent tiles a bit. Upon further examination I see that the tiles are not really adhered any more, as I could probably rip each one up with no effort at all.
So, what I want to do as it's easier for me to do myself, is put down higher grade peel and stick tiles. I do know that I'll have to put down an underlayment first because they will definately not stick to the flooring I have now.
My plan is to either rip up the old tiles or just lay the new floor over the existing floor. Regardless of how I do it (although just going over the existing floor would be easier), I was planning on doing a few things to make it easier on me:
1) I know that plywood is generally used as an underlayment, so I was going to get however many sheets I need, and possibly cut them in half, just to make them easier for me to work with. I'd rather deal with a 4x4 piece than a 4x8.
2) I was considering installing the floor around the toilet, making a template of the shape of the toilet. This is because I can't really be without use of the bathroom for too long, and lord knows how long it would take me to do this *lol*I know this isn't the best option, but would it still be ok to do it?
3) I was planning on doing the floor in sections, whether I remove the toilet or not. Our bathroom is a rectangle. Standing facing the toilet you'll have the tub behind you, with the toilet in front of you on your right, with two pedastal sinks to your left. I was planning on starting with the toilet section, putting down the underlayment, tiling it, but not going all the way to the edge of the underlayment, then removing the first sink to get it out of the way, putting down more underlayment, joining the seams, tiling it etc.. Then I would put the first sink back, then remove the second and last sink, put down underlayment and tile it.
I know that the best option is to probably use as big and as few sheets of underlayment as possible and do the whole floor at once, but that might not be the easiest option. Also, I know that usually you find the middle of the room and start tiling from there, but I thought I would draw an outline of how many 12" tiles are down on the floor now (or how many half tiles), and go with that same outline, so I can start in another area. Oh I would also remove the baseboard molding.
So is my plan doable? I also have just a few other questions:
1) Is plywood even the best option for underlayment in this case?
2) Do I have to prep it in any other way for the peel and stick tiles other than joining the seams?
3) What is the best way to secure the underlayment? Nails, staples, or screws? I've also read that they should be every 6 inches, is that correct?
Am I missing anything else? I know to some this might seem like possibly more work, but for me it may be a bit easier, being able to just lay alittle bit at a time, removing only one fixture at a time, putting it back, and then removing another.
Thanks for any advice!
Here is a picture of that lifting tile, so you can see possibly what material it may be and the flooring underneath:
www.handidrummed.com/bathroomfloortile.jpg