Searching for a narrow unit (i.e. 12" or less) will limit your options, as most all components are 17" wide, give or take a 1/2". And, you might want to buy used to stay within your budget. Also, the simplicity of inputs and lack of tone controls will also limit your options and will most likely raise the price higher than you want to spend.
A solution that meets your size criteria is the Bel Canto e.One S300i. High WAF, I'd imagine, but is costs 2k. Maybe you can find for 1/2 that, used.
The Creek Evolution 2 Integrated Amp is standard with but less expensive at $1095.00.
As you go down in price, an option is the Marantz PM5003 for $450. It's 17" wide and contains more features than you want. Also, the NAD C315BEE for $350 is another good one at this price point.
Good luck!
A solution that meets your size criteria is the Bel Canto e.One S300i. High WAF, I'd imagine, but is costs 2k. Maybe you can find for 1/2 that, used.
The Creek Evolution 2 Integrated Amp is standard with but less expensive at $1095.00.
As you go down in price, an option is the Marantz PM5003 for $450. It's 17" wide and contains more features than you want. Also, the NAD C315BEE for $350 is another good one at this price point.
Good luck!