The alphabet can be mind boggling, I agree. Maybe if you find someone who can explain how it works, in a simple clear way, like the stretching of letters to convenience for the pen or something.
Maybe try the oral way, for now?
Figuring out unwritten vowels is another catch 22. You have to know the word already in order to be able to read it, and then try to learn it.
Hope someone here has some good advice for you, I would like to know too.

I've been learning spoken Arabic by using the audio CD set for Egyptian dialect from Pimsleur.

I chose Egyptian dialect because Egypt is the hub of the Arabic-language entertainment industry, sort of like Hollywood is for the US entertainment industry. So most of the movies I'm interested in (ones with Samia Gamal, Tahia Carioca, etc.) are in Egyptian dialect, and also a lot of the great music is in Egyptian dialect. I certainly don't expect that my studies will enable me to understand a whole movie from beginning to end, but I'm hoping it'll enable me to pick up occasoinal things that aren't in the subtitles. Also, I've gone to Egypt 8 times, and will probably go again in the future, so that was another motive for choosing Egyptian dialect.

Anyway, I work with my Pimsleur CD's while I'm in my car, driving around town. Going to and from class, to and from the grocery store, etc. It's 15 minutes here, 15 minutes there. I'll work with a 10-minute chunk at a time, rewinding and repeating that chunk over and over until I feel I really have it mastered, then proceed to the next 10-minute chunk. At this rate, it could take me a week or two to complete a half-hour lesson, but once it's done, I feel very confident with what I've learned.

Pimsleur sells two different sets. There's a low-cost set that has 10 lessons. Each lesson is 30 minutes in length.

And then there's a higher-priced set that includes the same 10 lessons as the low-cost set, but ALSO contains 20 more lessons, for a total of 30 lessons.

I've been using it on and off since March 2008. Sometimes I'll go a month or 6 weeks without using it at all. So far, I've completed 22 lessons out of 30. I feel very comfortable with my progress. When I was in Egypt at the end of June, I felt VERY good about how much I was able to pick up when I heard people talk. Obviously, I didn't understand everything, but it made me feel as though the material in the course was good knowledge to have.

I haven't yet tried to learn the alphabet, but I'll probably start on that after I finish the 30 lessons on the audio CD's.