This will either take you a LOT of patience, or a LOT of coins, as well as luck, as you need to find a player item for each team in each league.
You can find a checklist here for Google Sheets to use to track your progresshttps://drive.google.com/file/d/0BwtkngobSgaJT0VXdEFsOXh6cGM...
The patient + Ultimate Edition method would probably be the easiest, as you would undoubtedly get a majority (hopefully at least) of cards to fill out most of the collection needs...and then after your 28 weeks of free HUT packs, go through and search for cheap players to fill in the missing spots.
Your other method is just to obviously just start dumping coins into each team/each league one by one until you reach the goal. This would pretty much be the only method available for non ultimate edition players who don't get the allotment of 'free' packs.
Needless to say, either way is a grind, with the 1st being slightly easier and more drawn out, but in the long run less costly. The only issue you are running into in both methods are NOT being able to find a player for a select team, which might be more of an issue with the first method as auction stock might be lower for obscure players as the game approaches 1/2 year from now.
Note that as of now it is damn near impossible to find ANY players online in the auction house for SHL, National, or Prospects...or when you do, its like the logo BS, where people are charging 20k+ for a freaking card.
Best of luck to all of you grinding this one out!