As with rods, it is possible to manage with only one reel, but if you do, I suggest that you get one with a spare spool so you can load it with different strengths of line.
There are different types of reel, but for a beginner a reel of the ‘Fixed Spool’ type is best. Perfectly good fixed spool reels can be bought for about £5 or £6, and if you can afford it, I suggest that you buy two, preferably with a spare spool each.
You will see reels described as being for ‘match fishing’, ‘legering’, ‘carp fishing’ and so on, but any fixed spool reel in the price range above will be perfectly adequate to start with.
You will probably find it easier to begin with if you buy two identical reels, and as this means the spools containing the line will be interchangeable, you will have more options too.