I worked in Costa Rica near San Jose for eight months a few years back. Lovely place and very tourist-friendly.
Sept/Oct. should be fine. I think that's near the end of the rainy season in San Jose, which means you'll have warm weather and daily rain showers (not continuous, though).
The Pacific and Atlantic coasts are quite different. Different fishing, different cultures.
Pacific side is best if you're looking for billfish, tuna, dorado, roosterfish, etc. Nice beaches and plenty of tourist activities.
Atlantic side is far less populated and developed. More of a Carribean culture, and fishing is focused more on other species (e.g., tarpon).
I fished out of Quepos on the Pacific side and found it enjoyable. Tons of sailfish. Prices for charters, even small boats, are steep, though.
There are tons of things to see and do. Jungle trekking, whitewater rafting, volcanoes, wildlife viewing, etc. San Jose itself is not particularly interesting for tourists. Food is mediocre, cultural attractions are scarce.
On the other hand, the people are great; figure out "Puda Vida" and you're halfway there to understanding the locals. Generally security is better than in most places. Petty thieves are about the worst of it. The police are generally honest and helpful. The government is a popularly elected democracy.
The road system is ok at best. BE CAREFUL DRIVING. The rules of the road are different. For example, people, even bus and truck drivers, will stop in the road and chat if they spot someone they know. People dart across the street and expect drivers to watch out for them. If you rent a car get a RAD4 or 4Runner; they'll survive the rough roads a lot better than a little sedan.
Go to a bookstore and check out the travel section. There are lots of books and maps available. The Lonely Planet books are consistently good. Also, start reading the Tico Times, the weekly English language newspaper. It has a fishing column each week.
http://www.ticotimes.net/index.htm
Use Google to search the web. You'll find just about anything you need to know.
One thing you should know is that Costa Rica doesn't have the native culture attractions you'll find in places like Guatamala. Most of the people are descended from immigrants (e.g., Germans, Russians, Spanish, Carribean islands). That's not a bad thing, but it's the reason I found it relatively boring, and went other places when I wanted an interesting vacation experience. My boss thought I was nuts to fly to Guatamala for vacation when she thought there was so much to see in Costa Rica.
have fun....Mike