What SQL Server database version do I need? I am not a database experts but part of the project I am currently interested in accepting requires to do a DB replication.

The system will have many outlets... says Site A, Site B, Site C, etc..

All sites will have a local DB, but only one of the site (says Site A) DB will be a central DB..

Other sites will push their data to Site A once a day (through intranet)....and it's only one way replication.. i.e. Site B does not need to receive data/update/etc from Site A or Site C... so basically Site A will be a hub and other sites will be client to Site A and they only need to push their data to Site A.... 

What kind of SQL Server edition for each of the sites (assuming that the size of the db is not so big - 10GB will be enough) I am thinking to use SQL Server 2008 R2. 

Also, What kind of replication does it require? Merge-replication?

from my understanding so far, I need


Site A: SQL Server Standard (or Enterprise)
Site B, C, etc.: SQL Server Express
Indeed Merge Replication seems to be the best fit for this scenario.
You can also check Transactional Replication with Updateable Subscriptions with queued updates, but it is less suited for situations where the servers are mostly disconnected, and the conflict detection is quite limited.

You are also correct about the versions you need: Standard or Enterprise for the main server, Express for the subscribers.