I live in the same area as you and have been a customer of the shop you mention for almost 2 years. In that time I've bought a baby beardy and 3 tawny dragons from them (2 female and 1 male) and had nothing but what I have thought is good advice.
In fact when I set up my first tank, for my starting lizards, a pair of tawny's the owner actually came around to help me set it up free of charge, as at that time, like you, I had no idea what I was doing and was having a similar problem establishing a heat gradient. (A thermostat and a change of bulb solved the problem).
I'm pretty sure if you'd taken your questions back to the shop you would have gotten all sorts of help and suggestions about ways to set up your tank. I also know the owner is pretty fussy about cricket sizes with baby lizards . .. . I got the lecture of my life the first time I tried to buy mediums by mistake for my baby beardy.
Good news is you got advice here I guess so you got answers to your questions somewhere, which is the main thing.
I use that same brand of thermometer in my beardy tank, and I've never had a problem with it.
I ended up going with a ceramic heat globe and a thermostat but they do cost a bit more money and not everyone likes to spend for more than the basics when starting out, though mine are in their second year and still going strong so I do recommend them.
Anyway good luck with your little baby. Watch out lizards are addictive.
Oh PS Do you chop up the defrosted frozen veg before you feed them to the lizard? Just wondering because I know some come pre chopped, but I don't think they'd be small enough for the little guy. Also just a suggestion but maybe if you added some other sticks and things to the tank as well the little guy would have more places to go than just the greenery.
