Should you call the missionaries? Absolutely not. They will pressure you and manipulate you. I would not call the missionaries unless you are sure you are ready to commence your faith-promoting, car-salesman, high-pressure jingle. They will have you read a book of mormon and coax you about the good and special feelings you have. They will tell you about how Joseph Smith restored the gospel and how you can be with your family forever. they will tell you the basic faith promoting things and pressure you until you commit to a baptism date. That's the best way to objectively get into the LDS church? No. You won't know what you are getting into and once you are in--and even before you have committed to join--you will be discouraged from looking at any so-called anti-mormon material. they will require long hours of your time and 10% of your money. If you like the high-pressure approach or being shielded from the "flecks of history" and such that don't make the church look so wonderful, by all means, call the damn missionaries.
That said, do your own research. There are many resources available to help you! A list to start you off:
Mormon.org and LDS.org are the LDS church's official websites. Pretty squeaky clean but you have a place to start. The basic beliefs can be found and you have access to the scriptures and ensign talks and articles which are useful resources. you can also contact missionaries through the sites if you wish to do so.
Fair is an LDS apologetics site. Mormon apologists try to deal with some difficult doctrinal issues and make them make sense.
Jeff Lindsay is a Mormon apologist and has some FAQ and junk on his site.
All About Mormons is a pretty good site.
Exmormon.org has information and stories form Ex-Mormons about why they left the LDS church.
The wives of Joseph Smith. Joseph Smith had over 30 wives. at least 11 of them were already married to other men when he took them as wives. this site briefly tells their stories.
Joseph Lied. This site is pretty simple and effective.
Richard Packham's site and this especially might be helpful in your investigation.
I might add more to this list later. it is in no way complete but I want to keep it fairly simple.
Where to start? First read some of the pro-mormon materials. read the official LDS sites and see what they have to say. Get an idea of the "official" face the church puts on but don't stop there. Look into the other side of th story too. check out Exmormon.org and read some of the stories of those who have left the church. look at the other exmormon sites and compare with Fair some of the arguments and see what excuses/explanations the apologists have. after you have read the arguments on both sides, if you still really want to join the church, use the LDS official website or ask a mormon to get you in touch with the missionaries. There are many people out there who are happy to answer your questions. I will be happy to help answer them to the best of my ability. of course, I am an exmormon so I am not going to have only good things to say about the LDS church. If you want to join, that's fine for you! Go for it! but make sure you know what you are getting into! Think for yourself and study both sides as much as you can. I don't think any mormon even would tell you that joining the mormon church is not a big commitment of your time energy and money.
You should absolutely look into the pro-mormon materials first. But these things are slanted in the most squeaky-clean and desirable way possible. The church looks like a delicious chocolate cake but if you actually break past the surface there is dog crap inside. The outside is delicious but when you break though the faith-promoting layer you find something you don't want to eat. Some mormons manage to break that layer but convince themselves with all their might that they are still eating creamy chocolate cake. the mind is a powerful thing. eventually many mormons are eating crap and going "mmm" all the way. It tastes bad but the cake still looks so good on the outside--who cares about the surprise filling?
Look at the outside of the cake. check out the LDS official sites and look into the church but I suggest you break into the middle of the cake before you have committed to eat it.
As pro-mormon material can be slanted horribly, so can anti-mormon material. I am not denying for a second that there are untruths presented to make the church look bad. But you don't even need to waste your time on those. The church's own "approved" but avoided material is quite sufficient for putting a bad taste in your mouth. There are numerous anti-mormon research websites that use even exclusively pro-mormon sources. I would challenge an investigator to look at the sources used. You can corroborate them with the official mormon materials. Sometimes it's hard to find or even has been changed in more recent versions of church publications but if you can get a hold of the source and read it you will find that most of the time it's taken right from the horses' mouth.
This is the part where many mormon apologists would accuse the info of being taken out of context. I say read what's before and after. most of the time the context is not being abused.
Can you trust the testimonies of Exmoromons? Exmormons come in all different shapes and sizes. Some mormons leave because they are disenchanted with the church's teachings as they know them. some have bad experiences that lead them to investigate further into the religion. I'm sure some leave for stupid reasons but almost all the post-mormons I have come across have been smart and able people who began to question and searched for truth, some more deeply than others. They find their very different paths out of the church.
Mormons often protest that these people did not have strong testimonies and were shaken because they were not strong. As for having your testimony shaken...If something is true it needs to stand up to criticism. That is the mark of truth. Things must be tested again and again and if they can survive the honest questioning and searching of a person who wants truth, they hold that much more credibility when they search is finished. In the end, people come to different conclusions. But as much as mormons might want to think that ex-mormons are the ones who were weak and did not have the strength to keep their testimony, I tell you ex-mormons are more often than not the ones who had the strength to challenge their testimony. The ones who had the strength to question and the learn and ultimately accept that the chocolate cake might not be so delicious.