You asked for affordable so...
I'm using "Fosi Audio V1.0G 2 Channel Class D Mini Stereo Amplifier for Home Speakers TPA3116 50W x 2 with Power Supply" to power my passive Avantone Mixcubes. (I'm guessing your 5cs have similar power requirements?) It's $50 on Amazon right now.
It works great. If I had it to do over again I would buy this one: https://www.amazon.com/Audio-Amplifier-Receiver-Integrated-Speakers/dp/B076P2VS9H ... $65.
The linked one has bass/treble which may be helpful. Obviously you bought these to have the frequency focus they have, but I wish I could tune mine a little.
Got it! Agreed I should hold off on sub but I'll make sure whatever amp/receiver I get has the sub outputs
Would either of these work with Wharfedale and future sub? I see RCA outputs and I'd assume yes? I've heard of Fosi but haven't heard of Aiyima do you have an opinions between the two? I don't want to sacrifice sound quality so open to other suggestions, or if you feel strongly the Onkyo would be best
https://www.amazon.com/Audio-Amplifier-Receiver-Integrated-Speakers/dp/B076P2VS9H
https://www.amazon.com/AIYIMA-A07-TPA3255-Amplifier-Digital/dp/B08CJZGT6H
AT-LP60X has a built in phono preamp > included 3.5mm to RCA cable > mini amp or compact amp or integrated amp or stereo or AV receiver > speaker wire > RCA passive speakers.
Mini amps: Ayimia A01 Pro or Fosi. Or Fosi with remote (has 3.5mm input instead of RCA).
Or a stereo receiver: Yamaha
Or look for a used stereo or AV receiver.
Plus speaker wire. Then How To Strip Speaker Wire and How to Install Speaker Wire.
Or instead of the RCA passive speakers, you could get powered speakers that have a built in speaker amp that connect directly to the turntable:
For $400 (assuming that is USD) total I would buy these.
https://www.musicdirect.com/equipment/speakers/wharfedale-diamond-225-bookshelf-speakers-pair
https://www.amazon.com/Audio-Amplifier-Receiver-Integrated-Speakers/dp/B076P2VS9H
https://www.amazon.com/Pyle-Phono-Turntable-Preamp-Preamplifier/dp/B004HJ1TTQ
Or if you want a speaker alternative which will have a more neutral presentation (probably one toe on the brighter side of neutral I would guess) rather than the warmer and more laid back sound of the Wharfedales, consider these which are on sale.
https://www.amazon.com/Polk-Signature-Elite-Bookshelf-Speaker/dp/B09B7XF3Z9
Can anyone also explain why a receiver/passive speaker set-up would be needed instead of powered speakers?
There's no reason why you would need to go that route... powered speakers would do the job. But you might want to go that route because the selection of passive speakers is much bigger than the selection of powered speakers. With a wider selection comes more competition, and potentially better price/performance as a result since you have companies trying to undercut each other. In your price range in particular I don't think any powered option can compete with the better passive options at the same price.
Once you hit $550+ you kind of reach the next tier of powered speakers (inclusing speakers that use active DSP tuning such as the Vanatoo T1 Encore and the PSB Alpha AM3) and passive vs. powered becomes a more interesting choice.