How to determine the value of the variable resistor to land on saturation region?
To set a hard upper limit consider that with the thing starting to saturate Vce will be small so you can figure the current in the chain (ignoring the drop in beta near saturation) as 15/(Rc+Re) near enough which I make to be right on about 6mA, 6mA in Re will develop 1.36V across it, so Vb(max) is just a nads over 2V, figure the divider ratio appropriately.