This is an odd one, I think Sky also buy the rights to the US Open from Eurosport. I'm not sure why Sky would drop this for the sake of the relatively small price compared to football rights, when the main UK audience must be more interested than usual with Murray and Konta high up in the rankings.
So:
Aussie Open - Eurosport
French Open - Eurosport
Wimbledon - BBC
US Open - ? Sky might release this back to Eurosport
Masters/500/250 - Amazon Prime
I currently pay for Sky, which includes Eurosport, but also Amazon Prime so I think I am covered, but I might drop Sky Sports if I can still get Eurosport.
Amazon Prime is predominantly used for getting free express delivery on Amazon products, it costs around £10/month, but it also gives you access to a fairly good online tv/movie service and a music service - I think it's quite good value.
Very exciting they should have done it earlier, obviously they now have plenty of experience of making cheap but high quality products using this platform; BBC 3 has allowed evolution of stuff that otherwise would never have seen the light of day. If the LTA engage in the right way it gives them a real vehicle to increase awareness of and build an interest in all levels of competitive Tennis.