There are two very good and reasonably priced preamps that will fill your requirements. The first, and in my opinion slightly better of the two is the Aesthetix Calypso. The Calypso is a tubed preamp that requires (for best performance) for you to upgrade the tubes to NOS tubes upon receipt. You should be able to find these new discounted to your price range and used for below your price range (used with good NOS tubes included). There is an upgraded SE Calypso coming out, so this is why you should be able to get the Calypso discounted new to your price.
The other preamp is the Capri as Guido referenced above. New you can secure these for under $3K without phono and used for just under $2K with or without phono.
I believe (just checked my Calypso manual, but it does not specifcy this), but I believe it is 100 ohm output impedence and does incorporate coupling capacitors to protect against dc leakage. Remote control is basically a full function remote with balance, input, volume, mute, etc. . .
If you need the phono card, the Capri is a better choice. You can add one to a new or used Capri direct from JRDG for about $500 and I understand it is a pretty good phono card. The remote is more basic with the Capri, volume, balance, mute, input (no power switch anywhere on the capri, if you want to turn it off you have to unplug it).
Be forwarned, the Calypso is a huge preamp and the Capri is a tiny preamp. Doubtful that has any impact, but thought I would mention it anyway.