What are the best entry level integrated amps and speakers?

So much of it is personal preference.  My bedroom system is a pair of B&W CDM2 Signatures I got on eBay for $350 and an old Arcam integrated amp I have had for 10 years or so.  I threw on some bulk Transparent Audio Labs wire I got a long time ago.  I guess they sold it for rear channels?  For $500 total system value, it sounds awesome.

Emotiva BasX preamp and Amplifier.  150wpc both for $600.  No bass management, but leaves enough to get very good speakers that don't need a sub.

Elac is getting so much press for being top performing gear, you must pay that some credence. Perhaps 50% of your budget goes to the speakers.
Right now on audiogon there is a steal on a classe integrated amplifier with a small defect. Original price $2000+, selling for six and change.

There is also an amplifier available now on Audiogon from Peachtree. It is their nova integrated with built-in DAC. I had a peach tree deco for a while, and it was great. The nova is even better! It is selling for 600 something.

add a pair of entry level kimber Or audioquest speaker cables for $150 and you have a fantastic system for $1500!

There’s a Rega Brio R here for $500 and a nice pair of slim tower Silverline Preludes at US Audio Mart for $850 (although you might be able to get this down a bit). The Brio puts out a strong 50W, and the Preludes are a pretty easy load so they should pair well. This still leaves $150 for some decent cables/interconnects. Excellent all-around performance and attractive with a small footprint, which I’d think a girl especially would appreciate. She’ll love it.  Heck, I'd love it!  Best of luck.

Stay away from NAD unless you want to buy a new amp next year. Serious qc issues. It will sound great then let you down.