That's a great topic for a persuasive speech, but it's hard to answer your first question. It's a highly opinionated topic and any ideas we contribute are definitely going to be biased towards our own views.
There are many ways to approach this speech, but if you want it be most effective I recommend you focus your argument on what the supporter's views are. If I were doing the topic, I'd probably focus on some of the healthcare and insurance differences between heterosexual marriage and homosexual marriage. After demonstrating there is a real disadvantage for them, I'd start exploring the reasons why people want these restrictions put in place. I'd spend the majority of the speech framing the opponents arguments before moving into my counter-argument. I could even go on to mention the fact that using religion as a basis for removing a persons rights is nothing new, people used to use Canaan (Genesis 9:18, 25, 10:6) as a means to justify slavery. One could even go as far as to argue that these restrictions are nothing more than a rehash of all the hate laws our society has been plagued with throughout its past.
In regards to your second question, try searching for ".edu" and ".gov" when you are looking for sources. These sites are more likely to provide useful information and they are typically subject to peer-review in one form or another.
Another easy way to find some reliable sources is to search the citations of the wikipedia article on a similar topic. You can usually find links to useful articles which may support your topic, but be careful! Make sure the citations it linked you to are the original source and that it is a credible site.