Ah, routers.
Small, medium, large, fixed base, plunge base, D-handle base, 1/4" shank or 1/2" shank bits, one-hand or two-hand, so many choices.
OK, I'll try to distill it down.
Bosch.
There, distilled.
No, seriously. Bosch is at the top of the line. There are others that may (or may not) be as good or better, but the Bosch routers are generally considered at or near the top.
Now, on to more specific choices.
We'll skip over the BIG routers for now. Usually those tools/machines are bigger and heavier and more powerful and more $$$. Great for mounting in a router table or for swinging BIG bits (like cabinet door profile bits, etc). Not usually considered a 'starter' router (unless you are starting a cabinet shop

).
A plunge base is great for plunge cuts. There are possible work-arounds to make a plunge cut with a fixed base router, and sometimes that is just fine and gets the job done and other times where you want/need a plunge base. For just edge treatment of the workpiece, a plunge base is NOT needed and just adds weight and height and extra things to deal with.
The 'palm routers' are physically smaller and lighter, and easier to handle. The Bosch Colt (older one without the LED or the newer one with the LED) is a pretty good router. Variable speed and soft start. It uses 1/4" shank bits. Which you can do a LOT with, just not hogging out big things all in one go (but you wouldn't want to do that anyway, as then you would probably have chip out and tear out to deal with. So you almost always take multiple smaller cut passes , even with 'big' routers). Price is around $100 give-or-take depending on sale and whether it's the older model without the LED or the newer pretty much same machine but a little more power and with an LED. You can get a plunge base, or a kit that includes the plunge base (
https://www.boschtools.com/us/en/boschtools-ocs/palm-routers-gkf125cepk-119901-p/).
Older model (but still quite capable, just a little less total power and no LED)
https://www.boschtools.com/us/en/boschtools-ocs/palm-routers-pr20evs-195774-p/
Newer one with the LED and a 'kit' with case and edge guide (handy for indexing off of the edge and then routing a groove away from the edge).
GKF125CEK
www.boschtools.com
Next up, the Bosch 1617EVSPK kit. You get a fixed base and a plunge base, so your bases are covered (pun intended). Can use 1/4" or 1/2" shank bits, so that is covered. Plenty of power for most bits (except for maybe the biggest cabinet-type bits, like a raised-panel bit. But you'd use those in a router table and you could take smaller depth cuts). Variable speed, which can be handy for bigger bit diameters or 'tricky' woods that burn easily (I'm looking at you cherry). Soft start, so the tool doesn't insta-jump out of your hands when you turn it on.
1617EVSPK
www.boschtools.com
A router table is handy, and sometimes required to make some cuts (physically or safely).
And the bits. Lots and lots of bits of bits.
(back in the day, a Porter-Cable 690 was considered THE general 'pro' router. Plain base, D-handle base, plunge base. But P-C is no longer the P-C of old AFAIK.)
I personally have the Colt (no LED) and the 1617 EVS kit, and an old Craftsman 1/4" that is annoying in some ways but hasn't died yet (currently mounted in an inexpensive small router table) and a DeWalt fixed and plunge kit variable-speed that no longer is variable speed (full-speed only now because the variable no longer varies

, hence the Bosch 1617EVS).
My suggestion would be either the Bosch Colt (handy and can do a LOT) or the 1617EVSPK (handy and can do even more than a LOT, pretty much anything you want/need to do with a router it can do with the appropriate bits and jigs and maybe a router table).
Skil (although owned by Bosch) is generally considered a lower-level tool brand (except for the top-line Skil-Saw worm drive circular). That router kit may be just fine and it may last for years (or decades, see above about my OLD Crapsman router that is still going), but I have no personal experience with that Skil router/kit. Just some other Skil stuff ( not the worm drive) that was definitely home-owner-level stuff.