Today I bought a used Squire Affinity P-Bass. It’s not a bad instrument but it’s old and been around the block so I’m just going to proactively gut the electronics before I set it up for C/C#. I want something doomy from the electronics—vintage alnico toanz with a little hint of modern. I’m close to ordering the EMG Geezer Butler EMG pickup set. I like this one because for $100 I get a set of nice noiseless bass pups with matching solderless pots and jacks so I can install the whole thing without even warming up a soldering iron. Anybody have a better suggestion?
Nothing at all wrong with the EMG pickups other than I think they might be a bit brighter in tone than you will want. Hard to say for sure on that.

I replaced the P-pup in a stock Samick P/J with a Dimarzio DP-122. It's a very well-made pickup; no junk here. The thing I noticed about it after installation was that it sounded somewhat "doomy" with nickel roundwounds. Darker than I wanted anyway. I put stainless roundwounds on it and the ss strings significantly improved and brightened the tone. I guess it depends on whether you like nickel strings. Or not.

Anyway, at $70 with free shipping the $30 savings over the EMG's will go a long way towards paying a tech to solder them in. Of course, buy the EMG's if you think that's the way to go.

Here's the link to the DP-122. Watch for a 15% off coupon to save 10 bucks.

Check out Bartolinis while you're at it. Also active. A bit less one-trick pony.
The EMGs can be a good choice since you are not plowing more money into the bass than the bass is actually worth. That's where the balance is going to be here. At someone point, you want to look at whether is worth upgrading that Affinity vs putting the money towards a better bass.
I agree with what anarkee said.

For the money you are putting into the EMG pup setup, you are then getting into the realm of maybe having something with a bit higher quality for the same money, more or less. I bought a Squier Vintage Modified Jazz Bass 5 string second hand for less than 300 bucks and it has a set of Duncan Designed passive pups in it that can get pretty much any kind of sound you are looking for whether doomy or bright. And as an experienced bass player, I was pleasantly surprised at the build quality and sound of the stock instrument. I prefer Rotosound nickel plated stainless strings because I play a fairly wide range of styles but the point is that your needs may be better served by getting a higher quality bass for about the same money.

That said, if the bass you have really inspires you to play and you really like the feel of the neck and how feels in your hands, then the EMG solution is probably the best way to go. I've had EMG pups on several of my guitars and love them.