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

Invest in good amplification first and improve your phono stage later. At your budget, I recommend looking at an integrated amp instead of separates. The ESL 57 is one of the best sounding speakers ever made so as long as you can find quality amplification to power it. I suggest either a Class A tube amp at least 25wpc (EL34 based ones are quite a great match with Quad) or a high current solid state amplifier. The 57s are very difficult to drive in the high frequencies, dipping to 2 Ohm impedance at 20KHz, so you’ll need a high current amplifier that can handle the impedance dips.

You might want to look into an EL34 amp that you can get for about $1K on the used market and save $500 on aftermarket tubes. That route may net you sonic performance of gear in the multiples of thousands. I cannot stress how important the amplifier quality needs to be for the ESL57 to perform their best. But when they’re controlled properly, you may never need another pair of speakers. Congrats on your gift!

Whether the 303 is a good fit will depend on how much the OP wants to put into maintaining the electronics. These pieces are very old (as old as the speakers themselves) and have been known to go on the fritz if they have not been recently restored. I’m assuming the reissue versions are not being recommended as the OP’s budget is too low. Considering the OP is a newer enthusiast, I wouldn’t push him down that way, either new or used. But that’s just me  

@arg6442 One thing about cloned amps is that they tend to use similar circuitry, but typically cheaper components, especially in tbe transformers, which add a cashier, more fatiguing sound. Unless you can demo the unit, or if the price is simply too attractive, it’s best to demo with the speakers before committing. While the ST-70 likely sounds very good with the 57’s, I’d suggest looking at more modern sounding amps. The ST-70 is a bit rounded and lush, which is not necessarily a bad thing, but paired with the 57s, you may find yourself wanting more on the high frequencies that you may not be able to get. 

I don’t always recommend them, but some of Primaluna’s offerings, a Rogue Cronus, or Quicksilver’s amps can likely do the trick. They are a bit more linear to match the 57s, and then you can tailor them with tubes of your choice down the line. There may be other brands/models, but they are eluding me. $1,500 doesn’t leave you too many choices for both an amp and money left for good tubes. 

For a decent phono for not much money, look into a Pro-Ject Tube Box S or DS on the used market. They can generally be had for $250-350, and spending $100 on better tubes will take you really far with them. 

For used gear, scan hifishark.com, which aggregates results from multiple online marketplaces. They even have a sold price that may give you some sort of idea of what an item typically sold for, or at least listed for before it sold. Keep in mind some are sold at lower than list.