Which is closest? Maybe Poas is the closest like El V said but I don't think there really is much difference in that regard than with Irazu (the bus transit times are exactly the same). Besides, they're both going to be basically half day trips whichever one you go to. Arenal is very nice but is in really in a totally different category than the other 2. Not only can you more easily visit Poas and Irazu from SJ, you can actually drive all the way up to their very tops and look inside their craters. Arenal CAN be seen in a VERY long day trip, but almost everybody will recommend to you that you spend at least a night there.
Which one is "better" to look at? That is really a matter of opinion, so I don't think anyone can really definitively say one or another is really "better". IMHO, each has its pluses and minuses. Also, you go to the first 2 volcanoes as much for their views of the surrounding country side as you do for the craters themselves. The Poas crater is more colorful and the surrounding area has more vegetation. The Irazu crater (and caldera) is more stark and, being at slightly higher elevation, offers more impressive views of the surrounding countryside (when the weather is clear). With Arenal, you can't go to the top, so it is much more about the view of the volcano itself rather than the surrounding area (its nearly symetrical cone form distinguishes it immediately as a volcano).
Some people also raised the topic of
how to get to the volcanoes. HikerTom mentioned the cheap way to get to Poas. The bus actually leaves at 8AM and arrives at Poas around 10AM (Tuasa tel#2222-5325). He is correct that it leaves from the small bus terminal across from Merced Park (and NOT the Coca Cola terminal which is a few blocks away). The good news is that it is also actually even cheaper than Tom said (1495 colones or ~$3 each way last summer not including park admission). The only problem is that Tom was also off a bit on time spent at the summit. It is actually much closer to 4.5 hours than the 3 hrs Tom said. (the return bus doesn't leave Poas until 2:30PM) and that will probably be a bit longer than most guys are going to want to spend even at a leisurely pace.
BTW, Irazu can also be done by bus and the bus schedules are actually a bit more convenient for that approach. Again the bus leaves around 8AM and arrives at the volcano around 10AM. This time the bus leaves from the corner diagonally across Avenida 2 from the National Theatre and the fare is a little bit more at 1790 colones each way (Lumaca tel#2537-2320). The good news is that the return bus leaves at 12:30 getting one back in SJ early enough in the afternoon for a round of the MP's.
Which touring companies to use for these sorts of trips if you want to pay a little more and go with an organized tour that will pick you up right at your hotel? I don't think it really matters. The easiest thing is to just book the tour through your hotel front desk. The prices and quality should all be pretty similar. A much larger question to ask first is what if any other sights you want to see along with the volcano. The volcanos themselves are interesting enough for an hour or two (or maybe a little longer if you want to explore a little further around the top on some leisurely hike) but you might find it to be a rather long drive for just a relatively short trip. Most people usually add on a few other attractions along the way (e.g. a visit to a coffee finca if you're visiting Poas or the Basilica in Cartago and the Orosi Valley if you're visiting Irazu. These make the day a little longer but it doesn't really add all that much on to the cost.
Personally, I think the best way to see either of these 2 volcanos is NOT by public bus OR organized tour. The problem with each of those is that you arrive at the top exactly at the same time as every other organized tour (or public bus). This is especially true of Poas which gets much larger crowds. For that reason, I think the best way to visit these places might be with a private driver (or rental car if you have one). That way you can leave a little earlier and get there before everyone else to enjoy in relative isolation and most likely with the best views. If you really have to have the tour guide spiel, then stay a little longer and tag along behind one of the organized groups after they arrive. But it is not really necessary to appreciate what you're looking at (Poas actually has a very good and informative self-guided tour center). Of course, the rental car or private driver could cost a lot more unless you have a few people to split the cost with.
Here are some other threads discussing these 2 volcanoes in greater depth:
http://costaricaticas.com/phpBB2/viewtopic.php?t=15676
http://costaricaticas.com/phpBB2/viewtopic.php?t=4959
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