Forget the 3040 type rubbish they are only just good enough to cut MDF and can't do that correctly.!

To me with your budget your only option is to convert the Mill and even then you'll have to buy wisely. If it was me I'd do it in phases and improve it as you go along and get a better fell for CNC.
Start by using the leadscrews that are fitted and just connect steppers to them, this is simple and cheap with minimal to no impact on the manual machine.

Controller wise then It's a perfect candidate for using Linux CNC because it's free and is scalable. By this I mean you can start simple with a Cheap £5 Breakout board and throw some half decent Closed-loop steppers on it which will be in £300 region and away you go, you'll just about do it with £500. Then as you have the money and learn you can build up the system and improve it with ballscrews and more advanced Mesa cards.
With Mesa cards and Linux CNC you can do just about anything, including using hand wheels for semi manual control(still need PC on). Clive S is the man for Linux CNC and he's converted the same machine using Linux CNC and it used handwheels.

I wouldn't look at any other route unless you substancialy increase the budget.