I always take twice as much of everything than I think I will need.
This includes spare insulin, needles, lancets, test strips, hypo treatment and insulin pens.
I also take a spare battery for my meter (I guess I could take a spare meter but never have).
I put my insulin in a clear plastic bag. This can be a different bag to the one with your shower gel, etc. and take it out in the security screening.
Regarding insurance, the most important thing to check is that your diabetes is covered. Some insurance doesn’t cover pre-existing conditions. Unfortunately, this seems to significantly increase the price of insurance but I think there is no point in having it if it does not cover the thing most likely to go wrong. In the past, I have arranged travel insurance through Diabetes UK. I think they have a broker they recommend.
Whilst you are away, you may need to test more often as you are likely to be exercising more and eating differently than at home.
I have read some recommendations that say to find out what “diabetes” is in the local language but confess I usually forget and have never needed it.
And, the last thing is to have fun. Budapest is a cool city.