In addition to the excellent points raised by Alex Clough, remember also that writing systems, just like spoken language, evolve over time.
For instance, consider a language that was originally logographic as it began to become a written language. Over time, as the language expands to incorporate more objects and -- much worse for logography -- abstract ideas, as well as begins to form a grammar to convey not only those ideas but the relationships between them, the writing systems will begin to evolve to correspond. The end result could very well be an alphabet based on an ancient logography.
Take the word "eye" in English. In a hypothetical ancient logographic version of English, "eye" would of course be represented by a drawing of an eye, which over time could have become simplified to look something like this: 𐍈. As the language later begins to evolve into one that is more alphabetic, common logographs could be drafted to serve as the new letters, specifically those that they start with: The '𐍈' logograph becomes the letter '𐍈', the first letter in the word "eye". Combined with the letter 'Y' -- itself a simplification of the logograph for a yak -- the word "eye" in this hypothetical version of written English is "𐍈Y𐍈". (NB: In this example, further simplification could result in the letter '𐍈' becoming the letter 'o', resulting in "oYo"; don't fret if you occasionally have a letter that looks like one from our own alphabet -- simple shapes, such as circles, just make sense to be commonplace elsewhere.)
Also consider the writing methods in use at the time in your conlang's history when it was first being written down: A brush and ink could result in sweeping arcs and stylistic calligraphy, whereas chiseling into stone tablets would more likely result in straight lines and stiff characters.
You can use a process like this to come up with histories for each of the letters in your alphabet, or symbols in your syllabary. Or, you can ignore all of this and just create something that you think "looks good": Nobody knows why the letters we use are like they are, and even the ordering of our alphabet (excepting some later additions at the end) is a complete mystery. You can always produce different letters from a single basic shape by using rotations and flips (dbpq), repetition (vw, nmg), small additions (OQ, rn) or subtractions (bh, EF), or minor tweaks (kx), any or all of which can help to unify the "style" of your alphabet. You can also follow the examples of ancient languages from our own history, such as simply omitting vowels from your alphabet like the ancient Phoenicians, which can help to make your written language stand apart from one that's simply a shuffled boggle of our own. There's no hard-and-fast rules for doing this, just ideas for how to get there on your own; I've been spending a lot of time myself working on my own conlang, including a unique writing system for it, so this is the culmination of what I've found for myself over the past year (off and on) .