First of all, this entire post assumes that the learner is sensibly learning Chinese first — that is, learning some of the language, and not worrying about literacy in characters until he has a base in the vocabulary and syntax of the language. Anything else is connect-the-dots in terms of writing characters; it’s just too much for the brain to process efficiently all at once. Language is the basic, universal human ability, not literacy.
As a self-learner, or even as a learner who is waking up and saying “I need to take responsibility for my own goals, because a group class may not do that”, you MUST start from what you ultimately want to do with your Chinese writing. If you’re in a group class, you need to focus on that. It may be necessary to say “I’m not going to devote so much of my energy to Activity X that isn’t getting me to my personal goals, and I may take a bad grade as a result.”
AFAIK, it has not been proven anywhere that writing out characters by hand helps with recognition. Think about it: those are two totally separate skills. One deals with being able to think about what a character looks like in detail and reproduce that form, using a prescribed sequence of strokes. The other only means you need to be able to recognize the character as distinct from all the other ones, with the assistance of context.
Think, too, that there is (there must be, or the whole thing would have fallen apart years ago) sufficient distinction between two similar characters for people to recognize that the patterns are different. Having to “scroll through” a mental list of strokes to get to the small difference before you can recognize the character is not going to help with reading per se. Being able to use clues of context, shape, and mnemonics to remember what a character is (and ultimately to be able to link the meaning to the written word in Chinese, which, unless your sole goal is to pass tests or win contests, is the whole point of reading) is more valuable for reading.
There may be benefit from writing charactesr by hand because you attend to (pay more attention to) the character when you do. But that is really just manipulating the character in some way. Having looked at other techniques used to teach early literacy to first-language learners, I’m not convinced that you would not get the same benefit from other types of manipulation of those characters (if you had manipulatives of the characters, or if you had them written on squares of paper and arranged and rearranged them, sorted them, played games with them, etc.) Writing is a particularly time-consuming form of manipulation that is not linked to the mechanics of pattern recognition in any meaningful way I am aware of. Why not explore other methods of increasing your attention to the features of the character you need to pop out at you for recognition?
Likewise, with radicals: there’s nothing wrong with learning radicals as a key to recognizing characters, since they occur in so many characters. But I would not begin by memorizing the radicals. I would get a list of the most common ones, and the ones that are most likely to help you because they will be apparent in the highest-frequency characters.
You can get a frequency list of characters (which is unfortunately distinct from the frequency list of WORDS used in spoken Mandarin) if you want to start with the most common characters. You could also think about learning the characters for the most frequently used WORDS first, but then you’d probably want to discount the characters/words that would not appear in writing a lot. In terms of “writing as a representation of speech” that wouldn’t be a problem, but if your goal is to read “real Chinese writing”, the frequency tables diverge more.
I still stand behind the idea of choosing the characters you want to write, and looking at them yourself. Notice (or look up) which radical(s) are evident, IF any are. Memorize based on those, if they are present. If they’re not, make up your own story about the character and its form and parts, and what it represents. The more bizarre or inappropriate those are, the better they tend to stick. This way, you are using the most effective of both worlds — the radicals, which will recur over the vast majority of characters, but are not always the key to remembering the ones you’re working with at the moment — and also using a proximal mnemonic for the specific character to make up the remainder. Radicals alone aren’t enough to remember (let alone remember how to write) characters.