You absolutely don't want grout there for a reason - when the plane shifts and expands, as it will, grout would crack open. That's why you use a colored silicon caulk that matches your grout (all grout companies make it). Don't use grout and cover it with caulk as this defeats the purpose and you'll just have a caulk-coated crack. Hang the bottom row of tile the same distance above the counter as your grout joints, and that joint will just look like another grout line: I'd agree re. the quarter-round trim - I'd fear wood would get wet too often in that area, discolor and ultimately rot away, or else hide wipedown crud underneath it as it loosens over time. :-/

If your long straightedge is bowing from the pressure of the router, you could support it in the middle by butting a two-foot-long scrap of particleboard (or almost anything, really) against the back of the straightedge and clamping it to the far side of the counter. That said, as long as the bow in the front edge is a smooth, even contour without abrupt jogs, it shouldn't cause any problem with the laminate. It might be better aesthetically if it were straight, but the laminate doesn't care if it's got a gentle curve in it. It's hard to imagine the counters are sagging on the sawhorses so much that they'll be permanently distorted by gluing laminate on them in that position. However, you'll need them fairly well supported for the glue up so you can lean some of your weight on the roller you use to press the glued surfaces together. For that reason alone it's worth supporting them well. You don't need a lot of sawhorses; I'd just put a couple of 2x4s on edge, on top of the sawhorses to provide even support along the whole length. You'll need to stabilize those 2x4s a bit, probably by nailing or screwing a couple of cross pieces between them, so they don't fall over flat at some inopportune moment. What size router do you have? There's nothing wrong with holding the router sideways except that you don't have practice doing it, and it could be difficult if you have a large, heavy router. The ones made for laminate trimming are small and light and can be held at odd angles with one hand. If you're stuck with a bigger, general-purpose router then it may be worth getting some help to set the pieces on edge as you described. You don't need a giant vise; just clamp it to some stable vertical object like a cabinet frame or the side of a sawhorse. When the clamp gets in the way, stop routing and repostition as necessary. Whichever way you go, if you've never done it before and you can't afford to goof, PRACTICE on some scrap!

If you want a glossy laminate, go Wilsonart instead of Formica. They have a much more durable finish. Either their Aeon or HD finishes will wear much better. I had an old display of Blackstar that was pretty horribly scratched up. It was where the stone countertop samples landed all the time because it had the best under cabinet lighting for viewing.

I just renoed a similar size home. Put new cabs with granite. No laundry though. $9k for remnants and chinese cabs. My last laundry room was $1k for ikea and laminate (probably less actually). Base budget for current build is $35k. A bit more square footage but it would scale down to $28k for you. So my suggested range is $10k to $28k. Helpful? probably not but really the best I can do. Add 20% for HCOLA. What you can do from plans is get linear feet of cabs. That helps. Island? Paint vs stain? Crown/end panels etc? Custom panels for appliances? Ceiling height and plan for uppers (stacked/tall uppers etc). But most importantly is expectation on door complexity and degree of customization.