You can use mastic or thinset mortar. I prefer thinset due to it not having issues with water. Though, mastic is very easy to work with and gives you plenty of working time. Thinset needs to be mixed and will set more quickly, so you have to work fast or mix smaller batches.
If you go with subway tile, you probably won't use spacers, they usually have built in tabs for 1/16 space for grout. Otherwise, look for spacers that match the tile width you want.
If you go with other tile, most cabinets are 18" above counter height (though definitely measure - I install mine at 19" for personal use) so if you have bigger tile, make sure you space it out so you don't have small cut offs at the top or bottom.
I like to cut most tile with a score and snap (not natural stone, wet saw all the way), but use a wet saw for multiple cuts, especially around outlets. If you need to cut out the middle portion for an outlet, to look like a "U", you make multiple cuts to the proper depth and the small thin strips of tile left will just snap off at the proper cut depth. If you are using bigger tile and need to cut only the middle out of a tile, you will probably need to buy some diamond tip hole saws (for your drill) or get tricky with trying to reverse plunge cut on your wet saw.
You can lay out your first row dry to make sure it looks good - you don't want to have 1/10 of a tile left on one end and a full piece to start, it can look poor.
Make sure you have plenty of sponges, water, rags, etc. to keep everything clean, and try to keep your tools clean of thinset or mastic. Use a rag to clean the trowel, they can be sharp! And if you get thinset on your handle, clean that up before you end up spreading it all over your kitchen.
Good luck!
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