I like peyote stitch a lot, it's faster then brick stitch for me, it's flexible, and it works well for a lot of graphing. But sometimes it's just a bit blocky for a pattern.
Choosing the right bead size can affect that because with smaller beads you have a lot more beads per square inch to get more detail, but the type of graph paper you use can also affect it. I have a lot of kinds of graph paper I've made up to graph designs. One of my favorite types is 2 drop peyote, which is just like regular peyote except you're going through 2 beads at a time instead of one. It does have it's limitations, obviously it's going to be easier to bead a multiple of 4 for an even count instead of a multiple of 2, and it's not good for things with a lot of sharp angles. Peyote definitely wins for geometric designs like snowflakes too. What 2 drop does well is softer things, the curves of things you see in nature and that sort of thing.
For an example, I decided on this photo I took of a raven because the shape of the raven is very clear against the brightness of the sky.

In the finished graphs, instead of the light pole, I put a branch under the raven, and did the background in a dark blue.
I decided on 40 beads high by 40 beads wide for both graphs. It used to be the standard for amulet bags.

Looks good, but see how jagged the lines around the head are?
When I did the same design in 2 drop, a lot of those lines smoothed out.

But if you look at the tail, you can see I couldn't do a smoothly angled line there.
I prefer the 2 drop model, you may prefer the regular model. A lot of the photos I take that I want to make patterns out of, what I'll do is overlay a couple kinds of graph paper over the photo in my graphics program to get an idea what type of graph paper will work best.
If you don't know how to use a graphics program with layers, or if you're just more comfortable with pencils and paper, you can still do the same thing. Use a light box, print out the image you want to use on regular paper, and a couple kinds of graph paper, lay the image first then the graph paper on the light box so you can see the image through the graph paper, and color in the beads. Some of the beads won't be completely one color or another, so on those, pick the color that's the majority in that square. You can fine tune your design after it's done. You can get project instructions for building a light box from our clipart host here.
Here's some blank graphs to get you started.