I'll try and assist - welcome to the forum!
There are a lot of reasons to choose either a Luminor or a Radiomir. It's just preference whether you like the ''onion'' or the locking lever. I will say if you enjoy changing straps the Luminor is far far more convenient. I might change my Radiomir strap twice a year, but my Luminor sometimes three days a week. If the Rad appeals to you there is no reason not to go in that direction. You will likely end up with both anyway.
Speaking for myself - I am not a fan of Panerai's in house movements. I will eventually end up with one, but I am putting it off as long as I can. Panerai service seems to be a mixed bag with just enough horror stories to make me skeptical. I prefer the older ETA based models as my watchmaker can service any of those easily and inexpensively. The newer movements have steadily increased in quality, but I remember the early 8 Day models running fast for a good number of forum members. I wouldn't spend extra money for 8 Days of reserve.
Given my prejudice for the older models and your size request I would be looking for a Radiomir 210. If you like the second hand there are so many Base logo Radiomir 380 models out there under $4,000 you could be picky about finding one. I noticed one dealer had six available alone. Neither the 210 or 380 are rare and you can find a nice one well under your stated budget even if you figure an immediate service into the price.
I have a Black Bay Red, and I believe you will find a Radiomir to wear about the same. The Rad will look bigger since the dial is larger with no rotating bezel, but the real estate it will occupy will be similar. I would take a photo for you in comparison, but I have a 232 and it is 47mm instead of 45mm.
I hope this is of help. There are far more knowledgeable Panerai fans here that will soon be along to add. Best of luck in your decision and again welcome!