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Radicals are the components of a given kanji. They represent basic concepts. There are radicals that represent "person," "heart," "water," "sword," and so on. Most radicals are also kanji by themselves. Alone, or glommed together, they usually help to convey the meaning of the kanji, either quite literally or by subtle metaphor. Usually, one prominent radical in the kanji is considered the radical for that kanji, and you can use it as one way of finding a kanji in a dictionary.
I think you'll find that you will coincidentally learn a lot of the most common radicals when you learn kanji in the usual school order, or in the order a typical Japanese-as-second-language textbook might teach it. For instance, once you know the kanji for "person" and "tree," you also know the radicals for "person" and "tree." They may be a little squished or rotated, but they're generally pretty similar. Knowing those two radicals would, for instance, allow you to learn and remember the kanji for "rest/break," because it consists of a person leaning on a tree (more or less).
Unfortunately, due to shifts in meaning, or in some cases where kanji have been written more and more sloppily over the years, the radicals in a kanji aren't always helpful in understanding its meaning, and you just have to memorize by rote. That's just life.
Stroke order won't help you learn kanji in any way I know of. It's a way of looking kanji up in the dictionary, so it's useful to know, but it won't help you learn the characters or their meanings.
I would recommend finding a well-respected Japanese-as-a-second-language textbook and learning in the order it offers. It will most likely give you a foundation that allows you to pick up new words/kanji by building on what you already know. You'll learn basic kanji, which tend to be radicals as well, which will then allow you to learn and remember new kanji, not to mention giving you a chance to guess at kanji you don't know by looking at their radicals and the context of the sentence.
Really, what you want is a combination of multiple techniques. Use a lesson plan created by someone with a clue. Use flash cards for things you won't easily remember. When you have time to kill, say the words and draw the kanji in the air. Read easy articles, manga, or books, and look up characters you don't know. The more different pathways you establish in your head, the better chance you'll have of finding a way back to what you're trying to remember.
(Disclaimer: I'm still only at 500-600 kanji, myself. I'm just telling you what seems to work best for me.)
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