Tile usually starts around 1.00 per foot, if you know the right places to search, you can get it for that amount or slightly more...but chances are it's going to run a bit higher, especially if you are aiming for slate. I'd guess in the 3-4 dollar range...but I'm not familiar with the pricing in your area...same goes for the labor. For slate or most natural stones I charge roughly 2.50 per square foot to install, sometimes more, sometimes less but that's probably the average. Normal ceramic I charge around 2.00 even....according to the particular job...it varies greatly...with stone, there is always either stone enhancing/sealing or multiple coats of sealer depending on what the client wants...and what the client wants to do themselves.
I've only installed maybe 6 different radiant heat floors...each one was different, and I had nothing to do with any them on the purchasing side. One of them was about 5x3, for a small bathroom, it was the type that comes in one piece...a mat...and I think the guy told me it was 75.00, but that was several years ago. I did a quick search...this one will give you a start...
http://www.radiant-floor-heating.com/electricexplained.aspx.
I'm sure there are cheaper ones out there.
My Great-grandfather and Grandfather installed one back in the 50s, it was copper tubing imbedded into what we call a "mud floor"....deep set mortar...the tubing was fed by a boiler system...as far as I know it is still in top working order. A few of the ones I've installed were of the coax cable size wires, and the houses they went into were not designed for a deep bed so I had to do it all with thin set...which is our standard mortar, and is not really made to use in any thick capacity...hence the "thin". But I begrudgingly managed....with many profanities cast about during....the mat one went in like a charm.
I do know of a ceramic tile site...that has members from all over the country...top notch installers too, they have a photo gallery...some of those guys are truly impressive. I think there is an installer or two near you...Seattle...I'll look and see, and if I find one I'll point him out to you...if just for advice.