I'm partial to Windows computers in general and for video astronomy. There are more software programs out there for Windows PCs than for Macs or Linux machines. Macs can function but you'll probably need to bootcamp into a Windows setup for video astronomy, depending on which camera you use. Sharpcap is a popular software program for video astronomy but it only works on Windows. Starlight Live has a Mac version but it only works with Starlight Xpress CCD cameras and there hasn't been much support for it lately.
Android tablets aren't quite there yet for software. ZWO is currently releasing a device called the ASIAir which will stream the images to an Android device. It's promising but it really needs "stacking" to be suitable for video astronomy (which they are working on). The ASIAir is basically a small, inexpensive, Raspberry PI computer that mounts on the telescope. It controls the scope's mount and the camera and sends images to a wifi connected tablet or phone.
As far as capability, it will mostly depend on your camera and how much software you want to run. If it's one of the smaller megapixel cameras, almost any computer will work fine. I've used an Intel Computestick computer with my ASI224MC with no problems. The Computestick (Gen 2 or newer) is a quad-core, Windows computer with 2gb of ram and 32gb of storage. It has an SD Card slot that you could use to bump up the storage. It costs about $120. The only caveat to it is it connects via HDMI. So you'll need a small HDMI TV or a monitor that supports HDMI. I've also used a Microsoft Surface 3 tablet (quad-core atom processor, 4gb ram, 128gb storage). Any windows tablet with a quad core processor should work fine.
For a larger MP camera like the ASI294MC Pro, a computer with an I3 or better processor is recommended along with 4-8gb of ram.
If you have a laptop or a Windows tablet, I'd recommend giving it a try first before thinking about buying a new one. You may find it works just fine.