Hell, we already have computing devices for most of the stuff you discussed, and it doesn't make amateurs into decent shooters.
I think OP was thinking more along the lines of a benchmount rifle than augmenting a standard rifle. In that case, this idea is feasible (but the price is probably a bit low). Let's do a very rough breakdown:
M14 (.308) - $1800*
Laptop - $1000
Optics - $2000 (good optics are easily $1000, and making is adjustable to read mirage, etc might double the price).
Servos - $300?
Stock material - $500?
Various gears / connection hardware - $500?
Fabrication costs - $0 (if you DIY).
Programming - $0 (if you DIY)
Total: ~$6000
*You could use a Barrett .50 for $8000 but the M14 shoots quite well at 1000yd
As with any project like this though, it's a good idea to double your budget for unexpected costs (~$12,000) and then double** it again if you need someone else to do the work.
So let's say $25,000 for a computer-controlled, 1000yd capable benchrest rifle, with lots of budget padding.
**I have no idea what this would realistically cost. Anyone know better than me?
Of course, you could always bring costs down by starting small (decent .177 airguns are ~$300) and learning from your mistakes before moving up to larger calibers.