TL;DR - buying gold mods with speed as a secondary will give you the best chance of getting very high speed secondaries.
OK here goes. This is my understanding of how it works.
The maximum a speed secondary can start at is 5. The maximum it can be upgraded to is 25.
Upgrading of secondaries on mods works the same no matter what the secondary is. When you upgrade, at levels 3, 6, 9 and 12, you will either reveal a new secondary or upgrade a previously revealed secondary. You can only upgrade secondaries that you can see when the mod is level 1.
Gold mods are the best. All secondaries are already revealed. You will therefore randomly upgrade one of the four revealed secondaries at each upgrade/reveal level. This is the way you get a +25. Speed has to be one of the four listed and it has to be randomly chosen for upgrade at each opportunity. It's very rare.
Purple are next. Three secondaries are revealed. You will randomly upgrade one of the three revealed secondaries at level 3, 6 and 9. At level 12, you will reveal the last secondary.
Blue up next. Two secondaries are revealed. You will randomly upgrade one of the two revealed secondaries at level 3 and 6. At levels 9 and 12, you will reveal the last two secondaries.
Green. One secondary is revealed. You will be guaranteed to this secondary at level 3. At levels 6, 9 and 12, you will reveal the last three secondaries.
White. No secondaries are revealed. You will reveal a secondary at each of the 3, 6, 9 and 12 upgrade/reveal levels.
So to get high secondaries, you need them to be already revealed at level 1. The position of the secondary has no effect on whether it is upgraded or not (so 1st does not mean better). This might come from the fact that if you have a green mod with speed as the revealed secondary, it is guaranteed to be upgraded so you'll end up with something in the 8-10 range. But doesn't mean it's the best.
Hope that helps and make sense. If anyone thinks I've made a mistake somewhere, let me know.
