performance versus order of fields in row

I'm not looking for an exact answer here, but instead something more
"rule of thumb". If I have a table with many fields, and I retrieving
small groups of fields during a SELECT, whereby the groups of fields are
indexed and/or clustered, will I get a faster select in the left-most
fields, or the right-most fields? Or will it not matter? It would be
unusual to SELECT *, I expect to be selecting groups of 4 to 16 fields,
and I am wondering if the most often occuring queries might be improved
by placing them at left or right ends of the table (or if there is any
help at all doing this). The selected groups of fields are unlikely to
be used as a search criterion, but instead as simple read-only, while
other fields determine if the row will be included.