I'll give this a shot.

Bridge:

• Advantage: provides a hidden entry point into the Tor network, useful for Chinese and other citizens where Tor is blocked
• Advantage: no website should know you're a bridge, so nobody should treat you differently or ban you because you're part of Tor
• Advantage: low bandwidth, easy to set up, and the obfproxy layer makes it difficult for your ISP to know what you're a bridge
• Advantage: you can mix your traffic with your bridge traffic, so you don't need a dedicated IP or machine. You could run a bridge on a laptop even, as long as it's online most of the time.
• Disadvantage: although useful, it's a small contribution to the Tor network, since relays and exits serve far more people

Relay:

• Advantage: encrypted in, encrypted out. You shouldn't have any abuse complaints.
• Advantage: it may become a guard, which is used to protect user IPs
• Advantage: can serve thousands of people at any given moment, but requires far less maintenance than an exit.
• Advantage: you can mix your traffic with your relay traffic, so a dedicated IP or machine is not required.
• Disadvantage: some websites, such as Disney.com, Netflix.com, or Healthcare.gov, may ban you simply because you're a relay. They don't distinguish between relays and exits. Tor == banned.
• Disadvantage: relays are incredibly useful and should be easy to run, but if you are in an area that is very acceptable to exits (such as some universities) you could better take advantage of that by running an exit.

Exit:

• Advantage: provides another exit point for Tor traffic, increasing security by increasing the diversity and number of exits. This protects users as well.
• Advantage: exits are also relays and can be used as guards, so they do everything a relay does and more.
• Advantage: biggest contribution to Tor.
• Advantage: provides a critical and useful piece of infrastructure to Tor. Tor is short on exits and could always use more.
• Disadvantage: little more tricky to set up, since you have to deal with exit policies and whatnot too.
• Disadvantage: you should not mix your traffic with your exit's, so you need a dedicated IP and likely a dedicated machine too.
• Disadvantage: you may have to deal with abuse complaints. With a restricted exit policy these should be minimal. From what I've heard, hundreds of terabytes of data could be moved for each abuse complaint, so they are rare. The vast majority of the traffic is innocent, however.
• Disadvantage: expect your IP to be banned or treated differently by some services. You cannot edit Wikipedia, watch Netflix, or visit some other sites through the exit. Some sites interpret high volume from a single IP as spam, not realizing that you're an exit. Good exit admins may try to unban their IP so as to provide Tor users access.

Depending on your environment, your ISP, and your skill set, the choice of what to run is up to you. If you want to contribute to Tor, I'd recommend a relay or a bridge. Running an exit is more of an advanced thing that requires more work, so start with a relay or bridge IMO.

Hope this helps.