I use an 11.1" (1366 x 768) small laptop Acer Aspire one, cost $289 a few years back. Runs fine for capture & control and operation of equipment and scope. Do not go overboard for mount and camera control laptop. You do not need great processing power to control a scope and camera etc.
You just need as many USB 2 ports as you can get, bluetooth and of course wireless and LAN and if lucky an RS232 port or HDMI port to output to a bigger monitor if later required. Of course capture control laptops need good battery life so get one with lots of battery cells...6+ or more, 8+ better.
I chose mine as it has 11 cell battery ....6~7+ hrs battery life and I hate ACER stuff but with these specs and battery life...I love it.
But if you want it for image manipulation software like Photoshop etc....totally different ball game you need to pay...MORE!
For a cheap option, ......maybe look at latest
ALDI Akoyo Laptop, $499 , 2 year warranty, 60 day return if you do not like if. Specs i3, 2.5ghz, 500gb HDD, 4GB RAM (can probably add a lot more as this is cheap) 2 usb 2 and 2 usb 3 ports, gigabit LAN wireless, HDMI, 6 cell battery, 64 bit OS but unfortunately WIN8. We just purchased one for our youngest in year 11...sto see her thru the last 2 years of school.
I'm sure win 8 is ok and can be made to run like a real OS (like WIN7) but atm it confuses the hell out of me.....here's me still using XP