A cycling-specific jacket, when rolled up properly, should easily fit in a jersey pocket. If it does not, perhaps yours isn't cycling-specific? In any case, with some velcro straps you can roll it up and strap it underneath the top tube.

Snacks go into a top tube bag, easiest place to access while riding without needing to stop and fiddle with.

You really don't need an oversized saddle bag unless you're doing a multi-day ride (either as part of light touring, randonneuring, or ultra-racing)... but if you really want to consider those, check out Apidura's racing line, or Topeak's Backloader line.