Budget system around 1K

So $1k for just amp and speakers? You will also need a phono pre most likely to I am guessing, since you mention the Rega.

One possibility might be the Audioengine powered monitors and a preamp...

OK I'll stick my neck out here:
I recommend the B&W 685s used, there is a great review on the TAS website. I own these and really enjoy them. There's a pair on ebay right now...
You need an integrated amp with a phono input. Currently listings on A'gon that I think would mate well with these B&W monitors:
Rotel's ra1062
Creek's 5250
If you can find the NAD c356, it would go well with the 685s also, and it has separate phono stages for MM and MC. Its a little more expensive tho.
Not sure how the Rega gear sounds because I have never heard it. I have only heard the above gear with a CD source, so consider that as well...Happy hunting.

Obviously s/hand will help a lot. Maggie 1.6 or earlier/Celestion sl6se SL600si or sl700si are wonderful. Certain B&W speakers, older Quad floorstanding cone speakers (not the electrostatics simply due to budget), Midrange magic. Totems tighter better bass, and perhaps a bit less magic.

NAD electronics very solid. good luck and pls keep us posted.

I believe the Rega Brio comes with a phono stage and for the $ is quite highly thought of. Epos speakers would also be a good match. Consider budgeting some $ for cables as well.

Onkyo A-9555, Vienna Haydn Grand.

A Rega Brio 3 would be a great option. It's a great little amp, and, while I haven't heard the phono stage myself, it's supposed to be excellent. Speakers are a personal choice, of course, but many people swear by all-Rega systems as excellent value for money, and the R1s are great and very unfussy about placement. Totem are also said to be a nice match with Rega electronics. A used pair of Dreamcatchers would fit your budget. If it were me, I'd keep my eyes open for a pair of Snell Ks or K/IIs or Audio Note AX-2s. I have an original Rega Brio and Snell K/IIs in my office (which together cost me $400 used), and it's a great setup.

Rega Brio 3 and R1 speaks would be great and well within budget. I am with you and the iPod thing.....however, I finally researched a lot and ended up with an iPod Nano 5th generation which sounds best of the lot in many people's opinions.

1) Rega Brio 3 is a fine option and has a decent MM phono input - there's one that just got posted for $425!

2) Energy RC-10 speakers (new at $300 - just posted). Find the SoundStage review!

...leaves $250-ish for cables and possibly an HRT iStreamer (one listed now for $160) to make your iPod a decent source.

Good luck!

Tandberg 3012 or 3012A integrated or Audiolab 8000A integrated (original British made not current), any of them around $300-$350. All have MM phono, not sure if you can run LOMC with them. I wouldn't. As for speakers..yes, older Snell or Audionote or some B&W. And some cables, of course.

Your "all-Rega" system is the joint. Don't deviate. Get a Brio (it's amazingly great with a killer phono stage), the Rega R1 and stick with your Rega TT. You will be happy.