Recommend an amp + pre for ESL 57s and a new turntable (way out of my league)

What luck, congrats, but you have heard 'be careful ..... bearing gifts',

That is a combo of 3 very unique vintage products that will require you researching, learning, acquiring a few tools and skills to get the best out of them.

Their age predicts maintenance may be needed as received or soon, so think about that.

I have inherited and been given some very nice equipment over the years, each is a fork in the road, chosen for you by friends and fate. 

I was given a Thorens TD124 with SME 3009 Tonearm, a wonderful combo, but I needed to restore both, and, when done, I found/learned the bearing design of the wonderful TT is very susceptible to vertical movement, and my wood floors are quite springy, so love it as I sat listening (after tip-toeing away), I had to make a change.

I still miss it, but, great as it was, it was not a good choice for this location. Are these gifts good you you and your location?

Those ESL speakers are special, however, most who keep them, to retain what they are best at, arrange the listening space around their design, and add supplemental bass, usually with it's own amplification. IOW, they are NOT full range speakers like you have had in the past.

Or, for some, perhaps you, your content, at not too high listening level, they are 'just what I always wanted'.

I don't want to be a downer, but don't rush in, you might want to sell these gifts and choose different speakers for instance, perhaps start with a good MM cartridge, move into MC moving coil and necessary pre-preamp later, and the TT, it is quite unique and it's parts are very old which is worrisome, perhaps it has been restored along the way, do you know?

The Moving Coil Cartridge's review

https://www.stereophile.com/content/miyajima-shilabe-phono-cartridge

It has specifics that I would not choose, it is what I (not everyone) consider a heavy tracker (lately I've gone from modern MC tracking at 2.0g back to vintage MM that track at 1.25g)

"It weighs 10.4gm. It's a low-compliance design designed to track at 2.5–3.2gm, which is unusually heavy for a modern cartridge" .

Do you have any knowledge of hours of play on it's stylus, or someone who can inspect it for you? I just won an auction at Yahoo Japan for a used AT160ml with beryllium cantilever, unknown hours, but I have Steve and Ray Leung at VAS just down the road to check for me.

I wonder how people think a Fisher 500C Tube Receiver (it has 16 ohm taps) would pair with OP's Quads?

I've been too lazy to take photos and list my Fisher 500c Tube Receiver for sale. I overhauled it, then had Steve Leung at VAS align it's FM Tuner. Mine is dead quiet, and has all the vintage features incl.  MM Phono, and a Tape Loop which could be used for a Chase Remote Line Controller to keep all the vintage features and get Remote Volume and Remote Balance.

I nor any of my friends have owned them, I have only seen/heard them long ago in shows in NYC

wiki about the speakers, several cautions about what type of amplifier

https://en.wikipedia.org/wiki/Quad_Electrostatic_Loudspeaker

excerpt

"

Its impedance is specified as ’30-15 ohm in range 40 Hz-8 kHz falling off above 8 kHz’,^[20] although another source states ’impedances are approximately 1.8 Ohms at 20 kHz but 60 Ohms at 150 Hz’,^[5] and its load is highly capacitive. It does not consume large amounts of power so much as it feeds it back to the amplifier in opposition at some points during each cycle. This is very demanding on amplifiers’ stability.^[17]

Although it is designed to be used with the QUAD II, 303, or 405 power amplifiers with limiters,^[21] a power amplifier capable of delivering 15 watts per channel suffices – excessive voltage input is known to cause arcing within the speaker panels.^[17] In fact, the instructions book states that any properly-regulated amplifier delivering no more than 33 V peak into any load is unlikely to cause damage to the speaker.^[21] Electrostatic speakers are more accurately rated by voltage, not power. In the ESL’s case, at the rated nominal impedance of 16 ohms, the limit of 33 peak volts would be reached when the amplifier’s power output reaches 15 watts (if it were driving a conventional load).^{[citation needed]}

The most common failure modes were loss of sensitivity caused by dust infiltrating the speaker panels, and internal arcing of the panels caused by excessive power to the step-up transformer;^[22] use at high altitudes may also cause the same effect.^[23] Also, because of its novel electrical characteristics, the speaker could cause some amplifiers to become unstable and could result in damage to either or both. Late in the speaker’s life, many owners found that the highly-stable 15-watt Naim NAIT launched in 1983 worked well with the ESL.^[24]"

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IF you need 16 ohm taps, that will limit your choices, my speakers are 16 ohm (but highly efficient), I tried and love this MK1 version which has 16 ohm taps (later versions 4,8 only), 22 wpc triode/45wpc ultralinear, and I found I like the sound of 6sl7 6sn7. Unfortunately, the bias adjust is internal, no bias meter. Perhaps people who have owned quads can comment if they think it would be a good pairing.

https://www.usaudiomart.com/details/650241412-cayin-a-88t-integrated-tube-amplifier-gold-lion-kt88s-nos-6sn76sl7-extras-excellent-condition/

You don’t see the version with 16 ohm taps listed often. I use mine with a tube preamp, (McIntosh mx110z) with MM Phono, and use a SUT for MC with Pass for MM. (Fidelity Research FRT-4). That SUT does not have an option that is good/ideal for the cartridge’s specs which I found in this old review

https://www.stereophile.com/content/miyajima-shilabe-phono-cartridge

"0.23mV (output) The internal impedance is listed as about 16 ohms."

You may need a MC Phono Stage with independent control of gain and impedance, FRT-4 has 4 options, but the impedance is resultant/fixed to the gain, the closest choice (30 ohm on dial) is xfactor of 18.27, the resultant impedance shown to a MM 47k input would be 141 ohms, a bit low for the formula target of 16ohms x 10 = 160 ohms.

This is why I suggest you consider a new MM cartridge now, save/check the gifted used MC, use it later when you know more and have had a chance to save for it.