Ahh I've started many a game with Liverpool so I hope I can help..
Basically what I try and do is, as soon as I can, offload the older/weaker players. Think for the future. The team isn't good enough to challenge straight away, unless your using a tactic made by someone. Personally I don't so.
Players like; Kuyt, Bellamy, Maxi, Carragher, Cole, Doni etc. All go for me. Bellamy is good for a season, 2 at a push. The rest can be replaced by younger/better players, who want less wages.
Also, make sure to sell Aqualiani when he returns in the second season.
Back to the future thinking. I try to involve alot of youngsters as much as I can. Spearing and Shelvey get alot of game time for me, as do Danny Wilson, Martin Kelly and Jack Robinson. I try to loan out the majority of others so they can get match time in the lower leagues.
First major signing I try and make is a striker, someone who can finish and isn't Andy Carroll. Usually for me, its Cavani. Get him at the beginning of your second season if you can. Should be able to afford him then. The amount of goals he'll get you is unreal.
First season, just make sure you get CL and also FA or League Cup. Brings in some extra money to counter act the massive wage bill. Try to renew peoples contracts, but offer less wages and better bonuses. Bonuses aren't a guarenteed payout every week.
Just a few more hinters. I find Suarez is quality playing as an Inside Forward in an AML role. Scores and creates for fun. Downing is poor, sell. After a good striker, wingers are top priority. Gerrard, Lucas, Adam and Spearing gives you good enough cover for DM/CM/AMC. Kelly, Flanagan and Robinson give good full back cover also.
Andre Ayew is a good signing. He's got a £11.25m release clause so not too expensive. If you can afford either Hummels or Subotic from Dortmund after a year or 2 aswell then your onto a winner.