Prepaids; They're all pretty much the same. Claro entered the market recently, and has been able to build a large customer base quick by putting out lots of offers with their pre-paid cards (more minutes for less pay kinda stuff, free calls to friends/family circle, etc.). However, don't base your choice solely on this. Ask your neighbors and friends what they use and how happy they are with the service, specially those friends you will be calling often. I also say neighbors, because there are some areas where some of the cell companies will have reception problems. Where we live, we had bad/no reception with Movistar and Personal. Claro has "better" reception here, but I've heard this same problem, the other way around, from friends that live elsewhere. Good luck!
I used to have Personal but in my area the reception was horrible, also I found it a lot more expensive than Movistar. I cannot say much about Claro but Movistar has great promos, eg one day per week if you top up 20 pesos they double it. But as 2GuysInPM said, definitely find out what works in your area. Though if you do not mind changing your number you can always try a different provider the sim cards cost 5 to 15 pesos and already come with some credit.
We have Personal, but we hate it. My husband's voicemail didn't start working until about 6 months into using it, the coverage is bad, and often we can't get into the voicemail system (about 30% of the time). I'm not going to go through getting another phone right now, but I wouldn't start with Personal again.
And in terms of trying another SIM card, youc an do that, but only with an open phone, which is much more expensive (unless you buy it on the black market). If you want to buy the cheap, pay-as-you-go phone, you have to purchase it dedicated to one provider.
I have Movistar for about 2.5 years now, it's decent. Good promos as with the mentioned double credit days. One thing I found out the hard way is that if someone calls you thru a VOIP like Yahoo or Skype from the US to your cell # they charge you for that incoming call. I have no idea why.