What ever you want to do. I would personally do what looked esthetically pleasing to me. I have a natural oak hallway floor, I used a black marble threshold for transition, then used my 12x24 staggered set porcelain tile in the Bathroom. I could have used the tile itself for a transition too. I wanted the threshold and due to this being a DIY, my options for fabricating the threshold were limited at the time. I had this black threshold or an ugly carrara option. All the colors look good together, aren't confusing as far as where one floor starts and the other ends. I wanted high contrast as the threshold is a bit elevated from the hallway wood floor. The contrast provides visual ques for people.

This is an in process photo that shows a bit of the floors and transition:
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Thanks, enduring. The threshold enforces the break and tells the eye, "This is a separate space." I also really like the staggered rectangles. You've been a big help!

On the bathroom floor, I would probably look for something sufficiently different from the (unavailable) hall tile so that it didn't look like a bad attempt to match.

Either butting the tile or using a threshold could work. My deciding factor would be that when the door is closed you shouldn't be able to see the adjoining room's flooring from the room you're in. So in enduring's example above, since the wood only came up to the edge of the door frame, the bathroom tile would have shown in the hall when the door was shut. So the threshold was a better solution.

I wouldn't match floor tile to shower tile. Too monolithic. I prefer variety. If you want to tie them together, then you could put a listello of the floor tile in the shower wall.

There are a gazillion options as far as size and layout. Choose based on (1) the style you're going for and (2) what appeals to you (go browse Houzz). If you've got it narrowed down, bring back your options and we can help you choose.

The only real "rule" is that unless you're using a threshold that spans the whole door frame, you want the two floorings to meet under where the door is when shut. Also, with respect to the threshold, it also serves a utilitarian purpose. Most people today try to build the tile up to be flush to the face of the threshold but this is actually wrong. The threshold was MEANT to rise above the tile to act as a dam in case of minor flooding.

Oh good, my threshold fits that bill, Bill, lol. I have not seen your post around here for several years. Hope all is well with you. You gave me a lot of help with my first bathroom!

I needed to take a break. Probably a good thing, too-- been working my tail off. :-)

I agree with Bill. A threshold, usually marble acts as a visual "break" between the two materials. It also acts as a dam to help contain any spillage from tubs, toilets, broken pipes, etc from flowing into the hallway.