I'm more or less a train enthusiast. I've helped people book Amtrak tickets from Southern California, but haven't actually ridden there. However, I commute regularly to work by Amtrak, so I'm familiar with their fare structure and some of the ins and outs of using their service. The Pacific Surfliner is mostly an "unreserved" train, meaning that your ticket is good any time up to a year as long as it doesn't get scanned (aka "pulled") by a conductor. There are some peak holiday periods where it's considered reserved, and where the pricing may increase.
The Metro Red Line goes from Hollywood to LA Union Station, although how close you are to a station may be an issue. It's a $1.75 adult fare and $1 K-12 student fare. I'm getting a typical 19 minutes from the Hollywood/Vine station to Union Station, operating maybe every 10 to 12 minutes depending on the time of day. If you're not that close to a light rail station, then it might not be a good option.
http://www.metro.net
I'm not sure if there's any kind of free transfer. Metrolink tickets also function as all day passes for other public transportation. So if you have a Metrolink ticket (it uses the TAP interagency fare card system on a temporary paper card I believe) you can also use that for connecting transportation like Metro light rail. I read that the Pacific Surfliner is supposed to have some sort of free transfer now, but can't find anything about how it works. On my rides, we can get a transfer good to use on several public transit agencies.