Ah, I remember my first plane.........
and my second plane.....
and.....
Sorry, was having a flash back.
Firstly,
buy some raffle tickets! You could win a plane and solve all your problems! (Shameless plug!)
As you plan to use power tools for the milling (I'm going to assume jointer and planer), you are past the "remove material and flatten" steps commonly associated with the Scurb/Jack and Jointer planes.
So, you are now in the realm of the smoothing plane followed by cabinet scraper.
You can equate a smoothing plane with a wide belt or drum sander.
You can't go wrong putting good money in a new smoothing plane. Lee Valley makes a wonderful tool.
Where you need to answer your own question is how much work do you wish to do to setup the tool. A Lee Valley/Lie Nielsen or other quality wooden bodied plane makers comes just about ready to use.
You won't have to spend countless joy filled hours fussing and fitting and refussing. Not to mention you get a mostly flattened iron ready for final sharpening.
Were it me (and by jove it is!), I'd advise you to take a whole different approach. One that is also far cheaper (initially).
Look for a jack plane. A used Stanley #5 (or other makers in the same general size).
Why? The jack plane is the easiest to setup and requires the least finesse to use. Its the hand equiv of the jointer and to some degree the planer. It hogs out the wood and makes it flatter (not flattest, thats the jointer planes job).
Plus, you can find them all over the place for no more than $30.
You gain almost nothing in buying a high end jack plane (when used for their original purpose). Sole flatness is not helpful. A tight mouth is actually a bad thing. The iron can be shaped with a 6 to 8 inch radius.
You also don't get into the "sharpen the iron till it splits atoms" that are more important in smoothing planes.
Being your first plane, I think you may find the finesse of the smoother to be a hindrance to learning how planes work.
I'd then use the plane to work on boards that you might find difficult to power mill. Be they too small or too large. When I started, I would just grab a board and play with it. Or make a few passes then return the board to the power milling machines.
Block planes are nice, but they introduce a different set of skills and are applied to different situations. They are small, and you'll likely find uses for them.
But, you may find you learn many of the same lessons from setting up and using a jack plane.
It also helps you get a better sense of what kind of hand plane work you want to do.
At least, that's my take on your "first plane".
Just don't ask about your "last plane"!
Jim