In a standard pattern, properly laid out tile should not wind up with a tile less than half thick at the edges.. maybe on the floor against a blind wall if anything. If you'd like me to explain a quick layout guide I can if that might be helpful.
Also, depending what you want to spend might help with suggestions. It's overkill for a small job, but HF does have a decent looking track saw for not a ton of money. Maybe post up pics or links to exactly what you are looking at. A small basic saw is really all that's needed, but if you have some kind of pattern in mind with alot of angles, a better model might help. The size of the tiles will contribute too.
12x12 marble tiles (I know I'll need a better blade than what they come with).
Right now, it's just a very irregularly shaped kitchen (picture below, the bay window is not centered in the room, you can see the door jamb is where I was standing to take the picture). I plan on laying the tiles as a diamond. I started heading that way because I couldn't come up with a good way of laying them square (no matter what there were going to be uneven sized cuts on the ends somewhere), but then I realized it just looks better anyway.
Eventually there will be 3 full baths...and then the next house when I likely move in 6 years (though I'll probably just sell it on craigslist after I'm done, more convenient than renting and not any more expensive).
What made me think I'll want to have a saw that can cut thin pieces is that the best layout I could come up with when I was going to do it square left me with almost no cuts other than some thin pieces that would go under the cabinet overhang (but unfortunately cuts at the entrances to other rooms that wouldn't be visually balanced)
Oh, and yes, I know my dishwasher will be captive by about 1/8" when I'm done. The countertops will be replaced by the end of the year, so worst case scenario if it breaks I will shut off the water to it and just hand wash for a few months.