What are the best entry level integrated amps and speakers?

Get a powered KEF LS50 and be done with. You maybe able to get one under $2k used.

I have 2 really great small systems that I expect to keep until the grave. One in the office and the other in the bedroom.

1) KEF LS50 passive + Peachtree Nova 150 integrated.
2) AUDIENCE - ClairAudient 1+1 v2 Bookshelf + Benchmark DAC3L + Benchmark AHB2 amp

The KEF LS50 is my favourite small speaker but the Audience speaker (2K) is incredible in the mid-range. They sound different.

#1) used is only a little over you price range. I bought both used for $2300. Though the price is likely lower these days since the KEF speaker is not the latest hot thing.

#2) is a lot more expensive, $7K. I just added it if anyone else was interested in a small office system.

Pipebro...It is always easy to recommend what each of us likes, but..............What is wanting her to upgrade ? What does she want more of / What does she seem to be missing ( imaging, coherence, neutral tone, dynamics, etc. ? What music does she favor ? What is her listening room like ? What are her sources ? Any shared walls / floors / ceiling. Sorry for my snartiness, but I need this information when helping people. Her e ya go.....Klipsch Heresy IIIs.

+3 for NAD

By all means don't purchase an amp and speakers without auditioning them in person, if that's possible. I'm sure you would advise your daughter about that. Some amps and some speakers match up well and others do not.
Here's a first hand example....
I used to use a HK receiver with a pair of Klipsch monitors. Those speakers weren't the lower of the Klipsch line but their top Reference series. The sound was OK but I decided to upgrade. I purchased a NAD integrated (C375BEE) and connected the Klipsch speakers. Sounded like a thick blanket had been thrown over the speakers and sounded much worse than with the HK receiver.
Then went to my local audio store and auditioned my NAD amp with a pair of PSB Imagine B speakers. The improvement of sound was astounding. So, proper amp/speaker match ups are essential.

+4 NAD/PSB setup. If you can get a used NAD375BEE with used PSB Imagine T speakers (that might cost a wee bit more than $1500 but not much more), your daughter will be in high cotton. Floor standers that match well with the 375. My sons use this setup in their room. I confess that I go up there and listen when they are spinning the vinyl because it sounds pretty darn good.