Binka's advice is spot on. And easy does it is the way to go on such a low, clear hot river. I notice you're coming from Lincoln, a fair drive. Are you a member of a club with water in the Shardlow area? I only mention it as, as far as I know, the stretches above Cavendish Bridge in Shardlow are Derby Railway AC, and those below are first Derby Railway and Then Pride of Derby, and neither do day tickets.
If you do decide to head out west towards Shardlow, you'll pass by Nottingham where you can fish two Trent stretches on a day ticket run by Notts Fed. The stretches are above and below Clifton Bridge on the north bank. further details on their website and Facebook page. Apart from the big-fish angling for barbel and carp, which is a nocturnal business, the general approach is stick down the side or waggler a bit further out. And of course, there's a couple of miles of free, easy access fishing on the Trent embankment above Trent Bridge.
I'm sure there must be some good day-ticket stretches on the non-tidal much closer to you, above and below Newark. You could check out the websites of Nottingham Piscatorial Society and Newark Piscatorials.
Don't ask me why the pretentious names, though.