Here's the basic history of character forms.
Oracle bone script
Chinese bronze inscriptions
Traditional Chinese characters
Simplified Chinese characters
The above are about Chinese script's history. A “script” is a system/style of writing. Script is not about font/typeface. Font and typeface are related to printing.
Also note, there are 2 distinct concepts:
For example, both traditional/simplified Chinese characters can be written in several styles. ⁖ cursive, regular. And a subset of the characters exist in Bronze Script (甲骨文) or Seal Script (金文).
Though, the 2 concepts are tied together. For example, Oracle Bone Script and Bronze Script are both about style and about actual character forms.
Typefaces is related to printing. For Chinese typefaces, basically all are variant of the Regular Script (楷軆 (Kai)).
In general, if you want a font with variable strokes as if written by a brush, look for a font name that contains “Kai” (楷軆). Otherwise, for normal readable text, use Song or Ming (宋體, 仿宋體, 明體). These are like regular script but more simple straight lines so it's more clear on computer screen. Font names with “Hei” is usually a heavier variant of Song.
For font comparison, see: Chinese Fonts Comparison; 中文字體比較.