Possible configurations for each email puzzle. The emails will arrive in the same order every time, but while listed below are the possible algorithm configurations, the solution is randomly shuffled around. Using this, you will be able to get emails 1-3 in 2 tries or less, and email 4 in most likely 2 but sometimes 3 tries.

1st email: 2 Ps and 1 BQP Make 4 Ps and 2 BQPs

2nd email: 1 P, 1 BQP, and 1 BPP Make 2 Ps, 2 BQPs, and 2 BPPs

3rd email: 2 BQPs and 1 BPP Make 4 BQPs and 2 BPPs

4th email: Will always have 1 of each, + an extra BQP or BPP Make 2Ps, 3 BQPs, and 3+ BPPs. Always do a set with 2 BPPs first, as you are constantly making them at that point. If one of them is gray, you have the 2 BQPs to use. If not, you can make an extra BPP.

So: It's the most reasonable to only make 8 Ps, 11 BQPs, and 7 BPPs. One extra of each is nice security, but any more than that and you are just losing time. Of course, it's likely that you will get at least one first try, so you will probably need even less.

Assuming normal validation rates, 8, 11, and 7 will likely cost around 43-45k info. Running algorithms generates some info, however, so the amount of info stockpiled that you need to start solving emails very safely should be in the low 30ks. Usually though, a number in the 27-29k range is enough, unless you get unlucky.