Better Integrated Amp?

The most important part of an integrated is how the volume control is implemented..  You can have the best electronics, etc.. but many manufacturers then use a cheap $5 pot for a volume control.. 
Be sure to understand what you’re getting in the way of a volume control.. it makes a huge difference..

You really should list your speakers and what type of music you play, but honestly, shopping in the $600 price range doesn’t leave you much room. The Denon integrated has been well reviewed, so maybe that’s your best option. There’s nothing wrong with the less expensive integrateds. I have an Onkyo A-9150 that was about $500 that is very nice and includes a phono stage and a DAC which is not horrible. Buy what you can afford and listen to some music. We all need to start someplace. All this said - sometimes we set a price point in our heads that is just not realistic. If you really don’t have the money that’s one thing, but sometimes we just get an idea of what we think we want to spend and it takes some time to get over the sticker shock of what the stuff we want actually costs. It’s all part of the process.

What is the rest of your system? 

Considerations:
   Budget
   Speaker sensitivity and impedance.
   Room size.
   Loudness levels.
   Use of digital as well as vinyl.