Newbie Question; security logs

[crzdgns1 at starpower.net]

Hello,

I have been checking my logs lately and find that a lot of access 
attempts have been blocked.  That's good.  There are a ton of access 
attempts, mostly from asia.  I am the only user on my computer, it is 
my home computer and I just wanted to try the whole open source 
phenomenon.  So far, I think IP firewall is blocking all unauthorized 
attempts to login, but, well, I am a  newcomer to freebsd/unix/internet 
security and want to be sure I am doing everything safely.  Some of 
my log entries say "possible breakin attempt".  That made me kind of 
uncomfortable too.  How do I evaluate whether or not my computer is 
safe?

Thanks

Mark