In the first season, you don't have to make any massive new signings, as the squad can easily cover a non-European season quite easily. It's only really quality you need to bring in, and young players to add depth for what should be a Champions League appearance next season.
A striker is your major priority, as Dirk Kuyt isn't getting younger, and not even a natural striker any more, and I've found Carroll to be fairly inconsistent. Who you want to pick up will entirely be based on formation. If playing with a single striker, you should get away with it, but injuries could seriously derail the season.
Henderson can play RM or RW almost better than CM, as his pace and crossing are very good. I played him here and found him to be far more effective than in the centre, where I had many more options. Retrain him up to natural in whatever position you use of these. Selling Maxi and using Henderson/Kuyt as RW worked for me. Kelly, and Robinson are both good stop-gap RB and LB respectively. I recommend picking up Otamendi from Porto if you have free cash though. He's max £13m, and is a top-quality CB for when Carragher retires/becomes less useful.