Welcome. I have been reading this forum for a bit, but I still think of myself as mostly a newbie, and I had much the same questions as you. But I thought I might try to help a bit, so here goes.
First off, follow any advice code65536 gives, or any of the Code Guys for that matter, as well as a whole bunch of other regular posters who know shloads about this drives. They will point you in the right direction.
Second, familiarize yourself with the various tools available for helping you get the most out of your drive. Kprobe in particular, it will help you see how well your burner is writing to different media. Also, visit the Codguys web site and give serious consideration to using the Omnipatcher and modified firmwares available for your drive. I have an 851S and I have modified it to act as an 832S and I'm using the CG4E firmware, and I couldn't be happier.
As for what media to use, I suppose it depends on how much you want to spend. I have had good luck with Ritek and Taiyo Yuden media, but some folks are wary of the Ritek stuff. I'd say go with the TY media, but if the price is too much, search through the media forums and see what results others may have for cheaper media. I have been using the +R media more lately, but I burned quite a lot of -R at first. I think I have beeter luck with the +R stuff.
As for your questions #2 and 3, why your discs may not work in all players, welcome to the world of DVD burning. There are quite a few possible reasons. The book type of the disc (DVD-ROM, DVD-R, DVD+r, etc.) may affect how the reader sees the disc. You may have a poor quality disc, or your current write strategy (in you drive firmware) for that disc may not produce the best results. And so on. Reading these forums will be a great way to learn all the ups and downs. And Omnipatcher can help you address some these issues. So the time spent reading up on it will be well worth it. Also, I use DVD Decrypter and CloneDVD quite a bit, and they seem to work great with this drive and with my media, so you should be fine there.
Smart burn is one of the features of your drive that you can read about on the Lite On site. It's likely on. Leave it that way. They intend it to help you have more reliable burning, and as far as I can tell it works fine.
Lastly, read read read. There is a TON of useful info in these forums. Learn how the search function works, and use it. Nothing wrong with being new, and having questions is natural, but being lazy will likely get you some nasty responses to questions whose answers could be easily found with a quick search.
Have fun with your drive too.