I want to implement SSO using Sharepoint 2010 with the following
scenario:

1. A server that is using an asp.net 3.5 application with the
standard ASP.Net membership provider (all the users will log in
using the membership provider database)

i.e.: http://membership.mydomain.com

1. A (remote, not the same server) Sharepoint 2010 server
running on some other subdomain.

i.e.: http://sharepoint.mydomain.com

Both servers share the same domain.

I want to implement SSO on the servers. That would be basically: If I
log in to the sharepoint server, I'll be also logged in the asp.net 3.5
application server and vice versa.

Any tips about this? Any links that could help me? Should I use claims
authentication for this?