I am a big proponent of taking public transit to and from NYC airports.

HOWEVER, in this case I think it is absolutely worth taking a cab. Taking a cab means you get on the taxi line, hop in a taxi, and 20-30 mins later you'll be a the other airport, at your terminal. The JFK website estimates $34 - $39.

If your flights are on-time you may well have the full 4.5 hours to kill and, if that is the case and you want to save $, then the Airporter may be okay. If your inbound JFK flight is late, however, you should take a cab.

Remember that with the Airporter you'll likely need to WAIT for the bus (not sure how often its JFK->LGA route runs) and then, once the bus arrives, you have to WAIT for it to leave and it may stop at multiple terminals before getting on the highway (JFK has 6 terminals and LaGuardia has 4). Unless you're lucky and the bus is right there, ready to go, when you walk outside . . . it could end up being 2 hours.

The Airtrain -> Subway -> Q70 bus that another poster mentioned is actually a pretty good, reliable option as well. It is likely what I would do. If you like figuring our transit systems with multiple transfers then go for it. However, since you've never been to NYC before my guess is that it may be more stress than it's worth.

I'll say it again that a cab is the fastest and least stressful route, albeit about $30 more than the other options.