FTTC: is it OK to switch off router?

[#1]

Following the latest episode of PN seemingly solving my very variable FTTC speeds (thanks PN), during which time I have left my PN technicolor router permanently switched on so they could monitor the connection (the BT modem is always left on), I want to change the router to get better, more reliable and faster wireless reception for connected devices.  Currently it is rubbish beyond frustration – over a few tens of feet in the house through plasterboard walls and chipboard floors.  What I am anxious to avoid however is disturbing the current stable (wired) connection speed.
Previously I have been told the FTTC speed can be affected by switching the router on and off and also the opposite that it should not make any difference.  What is the answer: can switching the PN router on and off affect the FTTC speed or its stability?   
Also any recommendations for a router with good wireless.  There seems to be a lot of choice, with prices varying by a factor of two or more for seemingly similar features.  If someone has had similar wireless issues and solved them with a better router then I would be interested in the model name.

[#2]

It's switching the Modem off & on than can give your grief. However you should always disconnect gracefully whatever you end up switching off.
Login to the Router and click Disconnect to drop the PPP Internet session. Wait about 30 seconds and then power it down.
If you need to turn off the Modem for an extended period, you can do it after that but wait about a minute or 2 after turning off the router.
But it could be better to switch the modem back on in daylight hours unless you are very close to the Cab. Wait until the modem has booted and sync established before turning on the Router. Log in and click Connect.