Recommended Pre-Amps under 1k?

The Parasound P5 was a very popular "budget" pre-amp, full of features that many/most pre-amps do not offer, especially at the price. If you are looking for a lot of features, like DAC, bass management, phono pre-amp, balance control, etc., it might be a good choice. However, in my experience (yes, I owned one), the sound quality is decidedly mid-fi. It just didn't have the type of hi-fi sound quality I desired. I did not need the added features, so out it went.

If I were looking for a budget pre-amp today, I would certainly consider the Schiit or Topping, especially if they had a solid return policy. Otherwise, I would probably look for a more vintage used unit.

Is remote required? There are likely some good older units in your price range that do not have remote capability.

Good points! And yes I would want a good remote. The Topping seems very hard to beat at a budget price. 

 Is a new preamp what you are looking for,or are you open to used?  I have found that buying used got me into some wonderful gear that I would have never even been able to consider on the new market. Maybe something to consider. 

For a grand I’m thinking the Schiit as you have already considered.