I think we may be a little confused about the end result, because you say 'Move'. I assumed you want to add a phone and internet connection, in addition to the existing. Not move the existing service to the new location(cottage)
If so, I see a few solutions:
1) run 2 lines- cat 5 or cat6 cables, the internet one would attach to a port on your router, or switch. Phone would tie in parallel to existing phone line. While cat3 would be good enough, it just makes sense to use better cable.
2) Wireless for both (or either) For data use a range extender, or access point (basically a second wireless router)
3) adapters to transmit the signal over power lines.
4) Wireless for internet, and use a voip adapter for phone (voice over IP) like this:
https://smile.amazon.com/OBi200-VoIP-Phone-Adapter-T-38/dp/B00BUV7C9A/ref=sr_1_1?ie=UTF8&qid=1467035754&sr=8-1&keywords=obi VOIP (Voice Over IP) would translate the phone (voice) signal over the data network (IP)
IMHO I would do #4. Wireless is easy, new phone line with a google voice number is basically free.