Matchbooks are harder to keep and display but worth more.
Flattened match covers are safe, takes up little room and can be displayed in plastic sheets. You can also collect both types.
Unstruck strikers are worth more. Front strikers are older & worth more than back strikers.

I started by buying "lots" on ebay. I also brought them home on visits to Nevada casinos. The best part about getting them from casinos, it's free!

Some recent covers are pretty scarce. Here's one from Golden Phoenix that I consider pretty scarce. I got it in November 2004:

I removed the matches thinking there are a ton of them (I have a full matchbook also). Does anyone have this? I found it laying on the counter of the unattended bar at the south end of the casino.

Match cover trades for Nevada casinos are available. I have tons of scans of my traders. Send email requests.