They are not difficult to cut with a diamond wheel electric tile-cutter. You need to cut them wet of course.
I have only experience of laying them outside as a path and a patio, but you have the correct approach wrt starting with the thick one etc. My concern is that whereas I was able to start in the centre of a patio and work outwards, or at the end of a path and work along, you have to start at some arbitrary point on the periphery and work around in a loop, as it were. You will have to take care that the slates will match up when you finally complete the 'loop'.
I take it you have already done the maths and come up with a design which won't result in embarassing odd bits of slate being added to fill unexpected gaps?!
You'll be using spacers I take it? 5mm are available: I used 6mm spacers of my own manufacture, but better to buy them ready-made.
You ought to check that your floor area is orthogonal [ square ] otherwise that could scupper any assumptions you made in calculating how to best cut and place your tiles.
I laid mine on a bed of tile cement ( from Wickes ), but getting the amount of cement correct to allow the tile to bed into place easily needs some judgement ( even with the five-spot method or using a grooved spreader.
I laid each tile flat with a spirit level, and as far as possible level with its neighbours. Slate being a variable material it is sometimes a matter of judgement whether it is, on average, level with its neighbours etc.
Check each slate is the correct size, is square, and is not too warped before you lay it.
I roughly cleaned tile cement stains up as I went along, with a final finishing clean with a sponge and a bucket of water at the end of each tile-laying session.
Andy