They are not pentecostal, pentecostal women aren't allowed to cut their hair or wear makeup, both of which all the duggar ladies do. i don't think they are baptist either. i'm pretty sure they are a conservative evangelical/charismatic family (as far as everything i know about them and i know quite a bit). they have church services in their home and other families attend. they are families that believe the same as the duggars and they worship together.
they teach their children that intimacy belongs in marriage and not outside it and a kiss can be very intimate, so it makes sense to wait and only kiss the one you marry. i love the modest bathing suits... i have always wondered why people don't wear their underwear for anyone to see but have no problem wearing bikinis that show more than the underwear. i don't allow my children to be so uncovered in regular daily life, why should it be a skin show if we decide to go swimming? swimming suits used to be full coverage for both men and women for just that reason, but over the years wearing nearly nothing and showing everything to anyone looking has become acceptable. i don't think it should be and i'm anxious to know where the duggars got those suits.
The Bible talks about children being blessings and a joy. There is a verse that refers to children as being quivers (or arrows) for the parents' bow (that being an allegory, of course). In other words, many children are a blessing. There is also a verse that encourages believers to fill the earth with godly children.
Now, of course children (whether you have 2 or 20) can or cannot be a "blessing" or "joy" exactly . . . It's not just to have many children, but to raise them in the Lord.
The Bible also teaches that life is given (and taken) only by the Lord. So, if a child is conceived and born, it is because God created that life and not the parents, per se. So by this woman having 17/18 children, it is because God allowed it in His power to create those lives through her. Therefore, if a family has 2 or 20 children, it is because God allowed it. The Duggar family sees the number of children they have to be God's decision, and they do not wish to control it.
The Bible also teaches that men (husbands) are to be head of the household, and that women (wives) are to submit to their husbands (as long as their submission does not go against the Lord). On the flip side (so that we don't confuse these teachings as an ugly dictatorship), the Bible teaches husbands to love their wives as Christ loved the church. How did Christ love the church? He loved them, cared for them, did what was best for them, prayed for them, and in the end He even gave His life for the church.