While the recent surge of research articles on sampling started with rather large sample sizes, it has later shifted to very small intervals, and it is now converging to intermediate sizes, and even to varying sizes. With 100M samples, warm-up is not an issue, at least with current cache sizes. However, with significantly smaller samples, warm-up becomes critical, especially when the sampling target accuracy is of the order of a few percent. However, in most sampling research works, warm-up has largely been treated as a separate issue. In this article, we advocate for an integrated approach at (simulator-based) warm-up and sampling. Instead of separating warm-up and sampling, we take exactly the opposite approach, provide a common instruction {\it budget} for warm-up and sampling, and we attempt to spend it as wisely as possible on either one. This budget and integrated approach at warm-up and sampling achieves an average CPI error of 1.68% on the 26 Spec benchmarks with an average sampling size of 288 millions instructions, and at the same time, it relieves the user from any delicate decision such as setting the sampling or warm-up sizes, thanks to the integrated warm-up+sampling and the region partitioning approaches.