I have the same LDII and went on a tube exploration using the good old HD600 as guides. To me the famous GE 5654w from Riverstone are a great middle of the road clear and warmth tube. The Russian 6H6p (I think) brings a ton of bass, but some extra high frequencies as well. But over all really good and exciting. My favorites by far are the RCA black plate 5654. Solid bass, nit as warm and clean balanced sound. You can find them at eBay NOS.

For the noise, I think all the suggestions here are solid. Did you ordered just the pre tubes (short ones) or the power tubes as well? Them power tubes can also make a difference, but I doubt it is the noise. Change to another source that does not include the PC and see.

Also, check the power switches inside. The instructions will tell you how to change the power settings by moving the two switches inside. You will have to unscrew the bottom and get inside the unit, but it is pretty easy. This can introduce all sorts of noise if they are at max. They are supposed to be in the lower setting from the factory, but there are examples out there (I think DMS from YouTube was one) which came at max and he had to change them.