Hi Redmannix1, welcome to the forum.
If you live in the UK, you are at the mercy of the NHS for your testing and, I believe, they will only test once a year, once you are on a 'stable' dose. However, you should try to get tested six weeks after any change in dose.
One important thing about tests, though, you should always, always ask for a copy of your results. If you live in the UK, it is your legal right to have a copy. Then, if you have any questions to ask on here, you can post your results, with the ranges, and make it easier for people to answer your questions.
Do you have Hashi's? If so, a gluten-free diet might help. Otherwise, eat what agrees with you, and what you like. But, try and avoid processed foods and oils. And no fad diets, like fat-free, or salt-free!
The most important thing to avoid is unfermented soy. And, that's difficult, because it's found in most processed foods - including bread. Soy protein, soy flour, soy oil, etc. should all be avoided like the plague.
As for supplements, you should ask your doctor to test your vit D, vit B12, folate and ferritin, and supplement accordingly. All these need to be optimal for your body to be able to use the hormone you're giving it. But there are some things you can take without testing - and maybe should - vit C, magnesium, zinc, selenium. But, always start your supplements one at a time, and leave a couple of weeks before starting another one.
If you have any other questions, don't hesitate to ask.