Hm okay, lots of info there.
Firstly for the reasons Attila has mentioned OPKs are not great for everyone. If you have pretty regular periods and have no reason to suspect any fertility issues then I guess they are pretty good for making sure that you have sex the ideal time. But in addition to the reservations that Attila has I would add that I understand it to be quite possible if you have a short LH surge and test once a day to miss it altogether, so not having a positive OPK is not necessarily an issue.
Also, I once used those internet OPKs and never got a positive, whereas Clearblue gave me a positive exactly when I was expecting it, so I question the accuracy of some cheapies.
The second point is that for many women, while the time it takes for them to ovulate might vary, the length of time after ov (the luteal phase) is usually a fairly constant length for that woman. An average range of luteal phase is 12-16 days, but it is not exactly unheard of to fall outside of that range. So if your cycle is 28 days this month, then it is possible that you might not ovulate until day 18, for example, if you have a 10 day luteal phase.
Yes, you are right to say that sperm can live a number of days. Some people reckon up to 7 days although I have read that after 3 days or so most sperm will be pretty knackered and useless. Therefore a good plan is to have sex every 2-3 days throughout your cycle so you don't miss ov.
Finally and most importantly (I should have put it first) rather than trying to work out your cycle, why don't you and your man just have lots of sex for fun for a few months and see what happens? You might not need any of this afterall! I have to tell you that each time I have conceived it has been after really fun good sex, so I'd focus on that and not the counting if I were you.
If you do decide you would like to understand more about how your cycle works, I can recommend Taking Charge of Your Fertility by Toni Weschler. I will be using her method as birth control in future and I find it really good to have a bit of a handle on what my body is up to.
Hope that lot helps. Let us know how you get on.