I do believe an integrated amplifier is the way to go at your budget.
I assume you are using the phonostage within the Denon receiver and the CD player as a stand alone. If this is true you will need a new phonostage as well. Also, if the CD player is working well you might want to consider the purchase of a new DAC and use the CD player as a transport via the coax digital output on the player.
One consideration is that Integrated amplifiers can be purchased as line level (amplification only) or with either an internal DAC and phonostage, or with both.
Another consideration is how much power you feel you need. Does the 50wpc Denon suffice?
Your thoughts on the above would help us help you.