Don't sign that many players, your team will need to re-settle, sign new players and look into specific stats like team work and influence is always one I look for when promoted.
Build a solid spine to your team, get players who will help you hold off the opposition, players who will work well together, same language and teamwork help here.
You say you don't need a goalkeeper, depending on who you have, look into Chris Kirkland or Scott Carson, both have PL experience and speak English.
Defender Right, would be worth looking into Nedum Onouha, Phil Bardsley, Habib Beye and Luke Young.
Defender Left, look into Emilano Insua, Fabian Monzon, Stephen Warnock, Jose Enrique and Federico Balzeratti [Palermo], and if you can afford him Andrea Dossena.
Defender Centre, always the most crucial for promoted teams in my opinion. You should look to invest here on players who will make an immediate impact, players like Brede Hangeland, Carlos Cuellar, Nevan Subotic, Paolo Cannavaro, Nicolas Otamendi, Bruno Alves, and Younes Kaboul.
Central Midfielders, Charlie Adam for a creative central midfielder, Wilson Palacios or Cheikh Tiote for a destroyer, and if you need an all rounder, go for Scott Parker, although he is pricey.
Wingers, players like Mauro Cameronesi, David Bentley, Duda, Diego Buonanotte, Pedro Rios, Juan Angel Albin and Christian Maggio all have proven well for me. Also, get Hleb if you can, very consistent.
For strikers in the Premier League, I feel you need a strong player to hold up play and a finisher. Go for Henry, he usually isn't interested in playing for them on Football Manager, should he be at them on your current save [New York]. Christian Benitez, Freddy Montero, Peter Odemwingie, even Ruud Van Nistlerooy are all possibilities, but can be quite pricey. The transfer list is your best friend, as are Man City, go for Santa Cruz and/or Jo from them, and if you can, Jefferson Farfan can do a good job up front.
