The minimal set of characters containing any stroke a Chinese character might have
Your answer should be looked up in calligraphic books.
If I'm right, you're looking for a set of Chinese characters or radicals with all kinds of basic strokes. You may know that basic categories of characters are heng (horizontal), shu (vertical), pie (left-slant), na (right-slant), zhe (curve or turn), dian (point, which may be a subcategory of na). Although there is one character that may cover all these categories (永"eternity", which called "永字八法" or "eight fundamentals in Yong" in calligraphy), it cannot cover all strokes if we divide the categories in detail.  I'll try to construct a set here to satisfy your need.  

Let's start by list one character per stroke:
0. basic -- 永
1. heng
simple horizontal -- 四
horizontal with slant -- 习 (as in President Xi Jinping)
horizontal with final hook -- 辽
2. shu
simple vertical -- 四 (included above)
vertical with final curve -- 四 (included above)
3. dian -- 永 (included above)
4. pie
simple left-slant -- 队
left-slant with initial horizontal -- 永 (included above)
5. na
simple right-slant -- 永 (included above)
6. zhe
vertical with final left hook -- 永 (included above)
curved vertical with final hook -- 辽 (included above)
horizontal-vertical turn with hook -- 习 (included above)
vertical with final right hook -- 民
curved stroke with final hook -- 民 (included above)
L-shaped stroke with final hook -- 匕
horizontal-curved turn with final hook -- 飞
3-shaped stroke -- 辽 (included above)
3-shaped stroke with final hook -- 队 (included above)
left-slant-horizontal turn -- 去  

Within seven characters, you get all strokes of Chinese characters.