First of all you need to decide whether you want a standalone/traditional chess computer which basically allows you to play only against the built-in AI or whether you want a more flexible solution which allows you to play against humans over the internet or to play against or analyze with chess engines or database software on a PC.
standalone/traditional chess computer
This includes the Novag Obsidian you linked or Saitek Kasparov or many others. As far as I am aware these type of computers have been largely deprecated in favour of PC/tablet/internet solutions. Still you should be able to find one new or second hand. With these types of computers the AI moves are usually indicated by LED, either on the side of the board (row/column) or by LEDs for each square. Apparently there is one (Phantom Force Electronic Chess by Excalibur) which even moves the pieces on its own, but does not have great reviews.
If you get one of these types of computers, make sure that the playing strength is sufficient for your purpose. Most of them can be beaten easily by somewhat experienced club players of say 2100 ELO or so.
The cheapest solution is to get a cheap board and pieces for around USD 20 and use a PC/laptop/tablet to run a chess program or to access an online chess site to play against computer or human players. Of course this would mean that you still have to transfer manually your and your opponent's moves between the physical board and the computer/tablet.
You can get rid of half the work, if you buy an electronic chess board ("eboard") which you can connect to a PC. "DGT" is a major manufacturer of these boards and they ain't cheap. With such a board your moves are automatically transferred to the computer and/or online web site. You still have to manually move your opponent's piecesthough. There are several systems for indicating opponent moves. In any case you could take them from the PC/laptop/tablet screen, but there also exist chess clocks (DGT Pi) which can display moves or chess boards with LED (Revelation II).
Playing strength is not an issue at all with any of these since modern chess engines that you run on a PC/tablet/... are stronger than the strongest humans.