I'm torn between the 1.5" and 1.75" sizes. Going to 2" might be better visually, such as for adding trees without interfering with the mini, or for placing more than one unit in a hex (subject to the 1 'Mech maximum), but then table space and weight start to become limiting factors.
Having a mix of straight and broken edges would suit me better than only one or the other.
1/4" thick is probably just thick enough to give a sense of height without excessive weight, although they could be 3/8" or 1/2" and I'd be fine with it. In the latter cases, it would look more impressive, but be less portable, heavier, and more expensive. Since the 'Mechs are definitely not to scale with the map anyway (otherwise the hexes would need to be around 4" wide), the height is fine.
As pointed out in earlier posts, there are plenty of better choices of material than Plaster of Paris. USG Hydrocal is cheap and about triple the strength of PoP, Hydrostone is along the lines of 5X the strength, while Merlin's Magic and Excalibur at the high end are even stronger (although the last is quite heavy and a bit more finicky on mix ratios, etc.). Woodland Scenics also sells "Lightweight Hydrocal" which isn't much stronger than PoP (it's likely to take some damage from routine handling), but weighs a lot less. Some people use Durham's Water Putty or expansion cement with good results. Resins are lighter, but cost a lot more and can damage the mold unless proper protective coatings are applied before each pour.