A relatively cheap amp that works great with them is the Luxman M12. It even has an "esl" switch.
An EXCELLENT amp for ESL-63s!! I have two of them, and a pair of the mono B-012s as well, and I've used them on '57s & 63s, as well as a number of other speakers. I had to go all the way up to Spectral DMA50s to improve enough to take the Luxmans off the Quads.
I've been using Quads since I bought my first pair in '83. I bought a second pair in '88, and they both still work, and neither has ever needed service! I did get a pair of USA monitors in the early '90s, and they were slightly better in some ways, but when I was tight for cash, I had no problem selling off the USAs (they had better resale value), and just using the originals... they aren't all that different.
If you can find them, I strongly recommend using Arcici stands on '63s. If you use Arcicis, the slight little difference in sound between the USA monitors, and the older, less ridged version almost vanishes if they are compared while in Arcici stands. They do really NEED stands of some sort, and the optional factory "Stand & Delivers" are OK, but they don't improve the speaker's rigidity, and they're not really high enough, IMO. The stiffer side rails are the biggest difference between the USAs & the older '63s, the changes to the protection circuit were very small, and retrofitable.
'63s are not particularly hard to drive, and they tend to make most amps sound good (unlike most other ESLs), but if you match them up with the "right" amp, there is real magic! They work well with modest push-pull tube amps too, like Conrad Johnson MV52s, Quicksilver monos, or even Dynaco ST70s, or MrkIII & IVs. I'd say, in general, around 30-60 wpc tube, or 60-80wpc SS is the appropriate power range for ESL63s.
Properly functioning, they will play very loud, as loud as any non-head banger would want... plenty loud enough for realistic orchestral works. No, they won't rattle the windows & scare pets like Infinity RSIVs, or such, but they don't need any bass enhancement to sound very full unless you have a terribly bright room, or are into Wagner at truly annoying levels. I don't tend to have "audiophile buddies" dropping by too often, but when I do, they are almost always "amazed" at how loud & powerful Quads sound. In short, don't believe the hype, these really are practical full range loud speakers
If you can afford it, I say GO FOR IT!!
I'm sure you won't be disappointed, and if you did decide they weren't right for you, you shouldn't have any problem reselling them once they have been properly serviced.