All you really need is a pair of active speakers. They're the ones such as the Edifers that OCUK sells. They have an amplifier built in to them. All that is required is a twin phono cable (red and white on each end) to connect the Ion to the speakers. Then use the volume and tone controls on the master speaker to change the sound.
If you want to do the proper Hi-Fi thing then you can spend anything from £150 to an utterly obscene amount on an amplifier and a pair of speakers if you wish. For a turntable such ss the Ion then either a Cambridge Audio Topaz AM5 or a Pioneer A10 amp would be a good match and a solid start for a really nice quality first Hi-Fi system. Each of those amps is £120. You would then add speakers. Wharf edale Diamond 9.0 are the usual go-to budget choice at this level. They're £60 a pair. Personally though I would spend a little extra and go for the Q Acoustic 2010 at £99. There's more bass and a sweeter tone which means they far more likely to satisfy you for longer before you have to scratch the upgrade itch.
Cheaper alternatives to both the amp and speakers exist. However, IMO they're very heavily compromised due to cost cutting so I don't believe they represent good value. The old saying "Buy cheap. Buy twice" applies accurately here. It's better to spend £60 on some decent active speakers than waste £80-£100 on a crappy amp and naff speakers that you then end up replacing after a year because you realise they're not that good even for cheap gear.