You can log the trial lesson but unless you know you want to do a PPL(H), I wouldn't bother with a separate log book. AN hour's flying here and there is, I'm afraid, a very bad way of getting a PPL - you'd waste money that way because you would have to relearn things each time you flew.
If you do enjoy it, save up and get a PPL in one go on a structured course (i.e. once/twice a week or full-time maybe?) but also have some idea as to how you would maintain the licence as well.
Above all - relax! Do not tense your legs and feet up on the pedals like I did otherwise, when you jump out afterwards, your thighs have gone all wobbly and you fall over!
Cheers
Whirls