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. Scriptures seems to indicate that those who choose celibacy (for whatever reason) 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 celibacy 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 writer of 1Corinthians 7 was aware of this, so although in he places the single state as being spiritually superior to the married state, he made it crystal clear it was not a sin to marry (1Corinthians 7:27 - 28).
According to what Paul says, it is not a sin to marry nor is the sex act itself within marriage a sin (1Corinthians 7:1 - 7). This last verse, as well as verse 2, helps explain why He said the married state was not a sin, but it was a lower spiritual state than remaining single. Interestingly enough, Jesus gave similar reasoning to the disciples when they questioned His condemnation of easy divorce laws.
"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 yes, indeed, those who are not able to receive Jesus' teaching on remaining single are not sinning when they marry to avoid burning with passion (1Corinthians 7:8 - 9).
In some of the verses you cited (1Corinthians 7:32 - 35), the apostle explains his reasoning behind encouraging believers to remain single. 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, but rather it applied in particular to the Corinthians who receive this letter roughly around 55 A.D. He still pointed out that he wished to spare people worldly troubles resulting from becoming married, however (verse 28), which is a universally applicable point. Jesus also did warn that those women who are pregnant or have to nurse children during the great tribulation to come would wish they didn't have those burdens then (Matthew 24:19), which is at a distinct time in history to come.
It is necessary also in this area, when the married state is compared to celibacy, to avoid thinking the married people are sinning, especially if they simply have trouble controlling their natural sex drives lawfully. 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. So the problem with the married state stems much more from all the special care and attention that a wife or husband needs from the other partner, as well as their children, if they have any, which takes away from time that could be used for serving God directly, not from the physical sex act itself. Marriage, however, should not be looked down on.
In conclusion, according to the Bible, celibacy is a higher calling than being married. As Jesus stated, those who are able to live a life as a single person dedicated to serving God should do so.