Starting at 0.25 means side effects tend to be mild or none at all for most people. Stay hydrated, keep eating something, and track how you feel week to week. The first couple months are the adjustment window.
Nausea on the starting dose is common, but vomiting twice in the same day is on the heavier end. Fatty or heavy meals amplify the side effects significantly on early doses. Most people find the first one or two injections are the worst and it settles after that.
The 4-week peak timing is worth knowing upfront - the first dose will feel like very little, and that's expected. The suppression builds gradually and the full effect usually shows somewhere in weeks 4-6.
The first dose excitement is real and tends to be followed by a lot of patience - the suppression usually builds over the first 4-6 weeks rather than hitting all at once. Starting the meal prep habit early like you mentioned puts you ahead of most people who start without it.