Here are some ways on how to effectively collect speedups for State of Survival
There are multiple ways and some give you speedup for an specific area for example troop training, so make sure what you need and focus on that
If you are looking for the best value to buy speedups then Deals Overview may be of interest for you
EVENT - Hunting the Hunted (Travis)
Every 2 Weeks you will have access to the event where you can locate travis, to collect speedups you can focus on collecting hunting rucksacks by killing regular infected. With travis leveled up one attack should cost you 8 stamina, 10 otherwise. The rucksack will give you 2-4 5m speedups.
So if you use full 200 stamina with lvld travis you will get a minimum of 4h worth of speedups that way.
Doing rallies on infected fiends will give you troop speedups. Depending on your damage it should give you 10-20 minutes worth.
Killing fiends will also give crates to the whole alliance which may contain additional speedups.
Using 200 stamina with travis will give you ~ 4h of troop speedups.
You can trade your resources against speedups by using the trading post in your settlement.
For each trade made you will get another trade offered -> so do all little trades to refresh
When you now only got offered trades that you don't want to take, refresh by using the "FREE" button on the upper right corner. This will refresh ALL trades with new ones
You get a number of daily refreshes each day so make sure you use them.
Being in an active alliance will get you morale speedups, you can complete various morale target to get and give out speedups.
You should generally aim to do enough of your daily missions to hit all reward target chests.
Its enough to just do so much missions till you got the last chest, additional will not give you anything more.
SPECIAL EVENTS & SURVIVAL OF THE FITTEST
You can also get some speedups on events like Survival of the Fittest or special ones like Birthday on the Ferris Wheel. But generally you also need to spend some to get them so its more that you get some small percentage back if you use them in combination with the events than a way to collect speedups.