Hi there. I agree with everyone who has asked you to first consider if you truly want to be married. Marriage is not something you should do in order to fit in or stop others from talking. It's seriously hard work. Everything changes when you get married.
Internet dating is good for introverts. If I were single now, I would find it very hard and anxiety provoking to go to a church and just meet people with an eye to date. I have a hard time befriending someone I want more with. I would have to go the arranged route or the internet route and be upfront with my intentions in getting to know someone, but that's me. And you don't have to change your quiet personality in order to date. You're more likely to find introverts online, obviously..
I found my husband on an internet dating site. We were not Christians so I am not going to give advice on something I don't have experience on. But I will share my experience on using the net as an early thirty something. Dating is a modern thing, and dating today lacks clear boundaries. Therefore it is very important to know what you want and state what you want before you get too involved with someone. Assume that anyone you meet online is meeting other people. (I did not do this but my husband was talking to another woman and met her after meeting me for the first time. Never met her again and quit meeting people after, but.. mentioning this because it's common) Now that I know Christians, I see them do similar things. So, I would advise to be upfront about a one-at-a-time policy because now more than ever dating is like a shopping market (on the net especially) and it's not about loyalty it's about novelty and self-satisfaction. Just something to consider.
If you do consider pursuing a dating relationship to marriage, also consider the person's spirituality. Just because someone says they are a Christian doesn't mean they share your commitment, so get to know the person well. Trust me, it can be tough when one spouse wants to spend 3 nights a week at church and more in personal prayer, and the other is only slightly interested. (I say this as a person married to a non-believer, so I have some experience here)
In general, if you date, just be able to say what you want, which is a serious relationship leading to marriage. Say what you are not comfortable with-- like, maybe close opposite-sex friends, ex's in the picture, or whatever. Do it when the relationship has progressed beyond initial chatting-- you'll know when an emotional connection is being formed, at least on your end. Don't let men try to mow down your boundaries, because some will try. (And they will apply guilt liberally when you remain firm!) If I were dating again and looking for marriage, I would be praying about it all the time so I could stay strong, because there is a lot of temptation and the arena of love relationships is fraught with it.. it can sometimes bring out the worst. God is more important than any of this, and I think it's better to be alone than to be married in haste to someone who isn't right for you. There will always be people who talk. When I remember to, I pray for them. They don't know the pain they can cause! God bless you going forward, and I hope that you find what your heart desires!