Jim:
USGA records show 32 entries in 1895, but 58 the next two years and 120 entries in 1898.
Wigham, who won the US Am in '96 and '97, was the medalist in '96 with 163 (two rounds, Shinnecock). Macdonald was the medalist the next year, with 174 at Chicago. Macdonald was again the medalist in '99 with 168 at Onwentsia.
I'm not sure if it's an apt comparison, but scores, winners and courses during a similar time period for the British Open (not Amateur) were:
1895 -- JH Taylor, 322 (including an opening 86) at TOC
1896 -- Vardon, 316 (including opening 83) at Muirfield
1897 -- Harold Hilton, 314 (rounds of 80 and 84) at Hoylake
1898 -- Vardon, 307 at Prestwick
1899 -- Vardon, 310 (with an 81) at Sandwich
That's a pretty good mix of players at a pretty good mix of courses.