For the grinder comparisons, use the search function on this site for the various grinders that interest you. Don't forget to read the two huge threads on this topic, e.g. the "Titan Grinder Project" and "Can it beat the Robur?", both of which I believe are to be found easily on the "Bench" forum. The comments below assume someone has enough money to buy whatever they want, regardless of price, and will make the choice based solely on functionality and not on price.
Bottom line on the grinders is that with planar grinders, the bigger the diameter of the burrs, the better. A general consensus would be that you have to go to at least 64mm and likely larger in order to get the "best" results. This rules out the Mazzer Mini, for example. With the Conicals, you have basically the Mazzer Robur and the Compak K-10 at the top. The conicals are huge, some (me) might call them ugly and out of place in a domestic kitchen, but have the advantage of greater grind consistency and the need for less frequent grind setting changes in order to get good shots with coffees as they age and with changes in ambient humidity.
In the middle is the Cimbali Max, which is a hybrid design using
both a conical and a large planar burr set. The planar burr set in the Max is used strictly for "slicing"/ e.g. grinding, whereas in a strictly planar grinder the outer part of the burrs are used for crushing (which is done by the conical burr set in the Max). The result is a much longer grind surface, which is coincidentally the advantage of the large straight conicals.
The Max will need much less frequent grind changes than a straight planar, especially the smaller straight planars such as the Mazzer Mini. As a result, you will have fewer sink shots. The larger conicals will have even fewer required grind setting changes, and perhaps slightly less sink shots than the Max, although at this level of grinder we are talking maybe 1 sink shot on the conicals per 2 weeks and 1 per week on the Max, assuming you are not changing coffees during this time period. The corresponding number for me on a Cimbali Junior grinder would be maybe 3-4 per week. As an aside, if you invest in a cheap 0.1g digital scale and weigh your grinds, you can reduce the number of sink shots dramatically on any grinder.
After you look at simply the grind product, you have to look at usability and appearance and fit and finish in a domestic environment. With those criteria, the Compak and the Robur fall down; the Compak on both appearance, fit and finish, and usability criteria, and the Robur on size and appearance in a domestic environment criteria. The Max is much cheaper than either of these, is easier to use (if you prefer the fine adjustment capability of the worm gear adjustment), and looks nice in a kitchen.
Alternatively, you could look at a large commercial planar grinder, however these (such as a Mazzer Major) may look out of scale in your kitchen and are not going to be cheap (as new), either.
But I do suggest you read the above referenced threads and use the search function. There is already more information on this site than you will need to make your choice.
As to the espresso machines, there is also extensive information on this site. Look over Dan's equipment reviews and use the search function. This will give you a much better idea of what is out there than simply reading posts from people recommending whatever it is that they have purchased for themselves. Finally, you don't necessarily have to box yourself in based upon criteria of whether or not a machine is to be plumbed in or not. There are ways to turn a pourover into a pseudo plumbed in machine later, and ways to use a normally plumbed in machine as a pseudo pourover. Rotary machine driven machines can be run off a bottle, and taking but one example, the drip tray on the Cimbali Junior does not need to be drilled, in which case you could simply dump out the drip tray daily or every two days, into the sink, as you would with a pourover. With my rotary Junior, I only plumbed in the drain after many months and instead simply put the discharge tube into the sink which was adjacent to it, or it could be run down into a gallon milk jug as another possibility, more or less what I'm doing with my old pourover Junior right now:
You could also consider doing some simple mods yourself, which may get you closer to whatever characteristics you admired in the GS3, at a much smaller cost and perhaps delivering a sense of accomplishment in the process. You would be amazed at what you can accomplish if you set your mind to it.
ken