As dan says, you can make a bid for players during the entire season and then the scout will tie up the negotiation letting you know if they said yes or no. If they says yes, it's just accepting and then the player will join your team as soon as the transfer window opens. It's a mistake to only make bids when the transfer window is open (it takes way too long time receiving an answer)
As to your question regarding a small team: I'm being one at the moment. FC Copenhagen. You'll see that they do have players with great potential - the rest you have to shop for
Try loan transfers and unknown/young players for the first season, since it's difficult to attract big players.
- And they have real kits