I've got an old 1989 Peavey bass amp 4x10 with Scorpion S-10425 speakers (still original 1989) 125 watts 4 ohms each.
Is it safe to put in new Eminence or Celstion 200 watt 8 ohm speakers in their place? And if I do this correctly, how would I rate the power?
I know nothing about this subject that I'm venturing into, and struggling to find the right google searches to answer my questions.
Since you know nothing about the subject, what are you basing these choices on? Why are you even replacing the speakers?
Note that if you're going to use the cabinet for *bass*, you may NOT want to use random speakers (choose bass speakers only).
Also worth noting that if you're dealing with bass, the choice of speakers is usually not necessarily done in terms of wattage, as it is with guitars. You'll want to look at things like Xmax, etc.

If you switch from 4 ohm speakers to 8 ohm speakers and wire the cabinet the same way it was originally, you'll end up with an 8 ohm cabinet. That's fine, but if you're using a solid state amp, you'll find that most will rate the power output based on the impedance.

Here's a typical stereo power amp:

1 CHANNEL RMS continuous
- 8 ohms: 500 watts
- 4 ohms: 750 watts
- 2 ohms: 1200 watts
BOTH CH RMS continuous
- 8 ohms: 340/340watts
- 4 ohms: 550/550 watts
- 2 ohms: 1100/1100 watts
BRIDGED RMS continuous
- 8 ohms bridged: 1100 watts
- 4 ohms bridged: 2200 watts

This is a pretty powerful amp, but note that the amp puts out nearly twice as much power into a cabinet with half the impedance. If you're putting 8 ohm speakers into a cabinet that normally carries 4 ohm speakers, you'll be cutting power in half.
I have been careful in viewing speakers designed specifically for bass. I'd like Eminence because it's what I'm used to.
I've been playing through a Behringer keyboard amp 300 watt. (4 channel 75 watt per channel) w/ a 15 inch Eminence. Blown a lot of speakers in this box but this Eminence is holding its ground very well.

Also, I want the cab in 8 ohms because I'd like to throw a 15 underneath. And at 4 ohms already I'm likely out of options aside from direct out into a powered speaker; I've done that before and just was not into it.

I've never heard of Xmax before.

Should note I am a budget musician. I generally buy my gear from zzounds or AMS. I use sweetwater when I have the funds though. So that's where I'm gaining most of my information aside from YouTube and forums.
I think you might want to go another direction, based on "I'd like to throw a 15 underneath." I'm assuming that you THINK that a 15" speaker will give you more low end. You're more likely to simply blow up the 15" speaker.

I've been using a fEARful 15/6/1 (well, two of them, and two fEARless F115s) for bass, keyboards and modeled guitar. The 15/6/1 has an Eminence Kappalite 3015LF 15" low frequency driver, a 6.5" 18Sound mids driver and a 1" 18Sound high frequency driver with wave guide. The cabinet will handle anything I give it up to around 900W, and it's an 8 ohm box. All of these drivers have neodymium magnets, so the whole cabinet is around 52 lbs (mine are actually a bit lighter).

Take a look at speakerhardware.com and find all the bits and pieces you need to build one of these. https://www.speakerhardware.com/diy-bass-guitar-speaker-kits/15-bass-guitar-diy-kits/ They have videos on the process and they'll no doubt shuttle you to greenboy.us to give you more information. This is a state-of-the-art bass cabinet (full range) using very high-end drivers that you can build yourself. If you are a "budget musician" you'll end up with a cabinet that will do almost anything you ask of it. The cab can easily be completed in a weekend, but plan on two if you're pokey.