ANSWER: Your general conclusion regarding what the Bible teaches is correct. Both Jesus and the Apostle Paul regarded celibacy as a higher calling than marriage. However, this begs another question. WHY are some called of God to stay single while others are not? Many men of faith in the Bible married. Some of these include Abraham, David, Noah, Isaiah, Peter, Job, Moses, Joseph and many others.
God's word indicates that those who choose celibacy, so that they could dedicate themselves to serve, include Daniel, John the Baptist, Elijah, and Jesus Christ. Part of the difference between those who serve and are married, and those who live lives of singleness, is due to each person's sex drive. God knows humans (he did make us) and will not allow us to be tempted beyond what we are able to endure (1Corinthians 10:13). The Apostle Paul was aware of this, so although he places the state of celibacy as being spiritually superior to the married state, he made it crystal clear it was not a sin to marry (1Corinthians 7:27 - 28).
Paul states it is not a sin to marry nor is the sex act itself, within marriage, a sin (1Corinthians 7:1 - 7). These verses, especially verse 2, helps explain why He said the married state was not a sin, but it was still a lower spiritual state than celibacy. Interestingly enough, Jesus gave similar reasoning to the disciples when they questioned His condemnation of easy divorce laws when he said, "For there are eunuchs who were born thus from their mother's womb . . . and there are eunuchs who have made themselves eunuchs for the kingdom of heaven's sake. He who is able to accept it, let him accept it" (Matthew 19:12).
The verses in 1Corinthians 7 merely make it clear that those who are not able to receive Jesus' teaching on celibacy are not sinning when they marry to avoid burning with passion.
In 1Corinthians 7:32 - 35, the apostle explains his reasoning behind encouraging believers to maintain their celibacy. He states that married people are more divided in their interests in serving God compared to the devoted single man or woman. In verse 26, he mentions the "present distress" as a reason not to marry, but that cannot be deemed as a universally applicable reason that applies to all Christians at all times. He is merely pointing out, given the state of the world when he wrote his letter, that he wished to spare people the worldly troubles resulting from becoming married. In a parellel warning, Jesus warns women who will be pregnant or have to nurse children, during the great tribulation (and not at other times), that they will wish they did not have such burdens (Matthew 24:19).
In these comparisons of the marital state versus celibacy, we should avoid thinking that married people are sinning because they were unable to control their sexual drives and therefore needed matrimony in order to handle their lusts. A single man burning with passion, even if he is not actually having sex with women (Matthew 5:27 - 28), sins badly, but a married man and woman making love to each other do not sin at all.
The biggest disadvantage of the married state versus celibacy is that it takes a certain amount of time away from dedicated service to God. Those who are married must spend time helping and pleasing not only their mates but also tending to the needs of their children. Those who are single, however, and unemcumbered by the care of a mate or children, can dedicate far more of their time and resources serving the Eternal than their married friends. Those who are able to live a life as a single person, dedicated to serving God, should take on this high calling and do it with all of their might.