I would like to pick out small objects from a category. I would like to find such a notion which


Dream 1. Picks out the schemes of finite type over $k$ from the category of $k$-schemes. Or at least picks out something relevant.


Dream 2. Picks out the top spaces homotopic to finite CW-complexes from the category of topological spaces (equipped with the Quillen model structure). (or something relevant)


Question: What notions exist for "small" objects (other than the compact objects)?


References or comments are welcomed.:)
Thanks!



Small objects in categories
The subcategory of spaces equivalent to finite CW-complexes is the smallest one containing a point and closed under finite homotopy colimits. (In fact, this is the universal homotopy theory generated under finite hocolims by a single object). 


Someone more patient than I could might fill in the details to make the following sentence both (i) sensical and (ii) correct: If $G$ is finite, the subcategory of $G$-spaces equivalent to a finite $G$-CW-complex is the smallest containing a point and closed under finite 'enriched' (weighted is probably the right word) homotopy colimits. (Here I'm enriched in $G$-spaces instead of spaces like above). 


The category of schemes is probably too ugly of a place to try and make a similar statement, but perhaps one of the many colimit-populated enlargements would allow you to make the statement that some reasonable enlargement of the category of schemes of finite type over $k$ is generated by a point under some allowed collection of colimits.


(By the way, in the first two examples, honest compact objects are obtained by idempotent completion, i.e. adding retracts.)


