One dire mistake is the idea of Peter being the first Pope. Peter was not a Pope, he was an Apostle. Peter was not a Bishop, he was an Apostle. As we know, our friends the Catholics say that a Pope is a Bishop, a man that is ordained to be the chief bishop over the whole Catholic church. All of their bishops allow this one bishop to govern, and that is fine. But as far as Peter goes, he was the head of the body of the group of 12 men who were ordained apostles by Jesus Christ himself. Jesus was ordained by His Father, which is referred to by Paul as being ordained after the order of Melchisedec. (Hebrews 5:6) If there was to be a man, or a group of men, who wanted to claim any authority that Peter had, they would claim to be apostles, not bishops. Bishops are an office in the hierarchal organization of the church, but not the head. They were to look after the local needs of the churches, not to govern the church as a whole. That was the role of the apostles. This is why the apostles traveled all over the known world, wrote epistles, had revelations, performed miracles, etc. - to support the roles of the local leaders, the bishops, priests, deacons, and so forth. Of course, we are well aware that most would claim there were only 12 apostles and there can be no more (which logic is faulty by the way, since they ordained Matthias to be an apostle after the death of Judas, and some time later Paul became an apostle), so anyone who claims that there are no more apostles also claims that there is no one ordained after the order of Melchisedec to run the church as a whole - which would stop revelation, and we would be in dire straits indeed!
One thing to be careful of is that we often think we can read the Bible and assume we have authority, or assume that it is a complete record of every doing of the church, or that it contains an exact priesthood manual for easy reference on how to govern the church. The epistles by the apostles in authority are letters. Letters written to very specific people for very specific topics. They are by no means an exacting list of the hierarchy of the church and a manual on how to perform your priesthood duties. This is why many have confusion, because they are looking for information that just isn't there. Who has the correct information? Well, the apostles who are ordained by Jesus Christ would be the place to find that.
As far as marriage goes, and again, the Bible isn't a manual on how to get married, what to say, how the ordinance is performed, etc... but we can try to extrapolate what was mentioned for our benefit, but we must be aware that there may be pieces missing. What it does mention about marriage is that it is not good for man to be alone, that a husband and wife should cleave together and be one just as Jesus and His Father are one, and that a bishop should be a man with a wife, one wife to be exact. Nowhere is plural marriage forbidden and thus it was practiced by many. Abraham had his wives and Jacob has his 4 wives. They were greatly blessed as the whole of the house of Israel is based off of these polygamist marriages. All these things are easily found in the scriptures if you search marriage, so do yourself a favor and look them up.
One scripture I will give you, since your topic is specifically about the celibacy of priests - which is not taught in the Bible, but what Vale of Tears calls an inference of scripture, which is dangerous due to the incompleteness of the records - anyway, here is what the record teaches us. Paul warns that there will be some that shall "depart from the faith... FORBIDDING TO MARRY, commanding to abstain from meats...", etc. If a church is teaching you to not get married because somehow this makes your priesthood office less effective, then you know they have departed from the faith, for it is not good for man to be alone.
So what did we learn today? We learned that Peter was not a bishop, he was an apostle. That there were at least 14 men that we ordained to this office, so anyone trying to tell us that there were only 12 has their facts wrong. We learned that Paul was an apostle and since he was not of the original 12 chosen by Jesus, that this body of 12 men was meant to continue when one was killed or left the faith. Matthias was the 13th apostle, chosen to fill the hole left by Judas' death. Anyone who claims that Paul was an apostle, must by default accept that the apostleship would go on and that the church would have apostles governing it forever.
We learned to be careful while reading the Bible. To be aware that everything is not there and to make sure we understand the scriptures in their full context.
We learned that God condones marriage, though he may limit a bishop to having only one wife. We also saw that Paul warns that there will be departures from the faith where people will command others to not get married and for some crazy reason they will tell people to abstain from meats. Sorry vegetarians, but that's what it says!
Finally, after Paul lists the hypocrisy and false doctrines (such as abstaining to marry), he says, "If thou put the brethren in remembrance of these things, thou shalt be a good minister of Jesus Christ, nourished up in the words of faith and of good doctrine, whereunto thou hast attained."
Remember these saying brethren! We know true and sound doctrine! And if some church or teachers try to teach you otherwise, you can clearly discern their departure from the faith taught by Jesus and His apostles.