They are all on the north side along the lake. Lincoln Park is furthest South, then Lakeview, then Wrigleyville as the one furthest north. For the most part, in Chicago, the closer you are to downtown and to the lake, the better. So they are best in that order: lincoln park, lakeview and Wrigleyville.
Lincoln Park - rich mature people, young couples until their kids need to go to grade school, college kids. Most upscale of the three.
Lakeview - retired people, gays, college, just about anybody lives in lakeview.
Wrigleyville - the most varied of the three with lots of college kids, and young adults going to work