I would have to strongly recommend 2 series.
The first is GMT's Great Battles of History (GBoH). Everything from Ancient Egyptian vs Hittites in Chariots of Fire to the Mongols in Devil's Horsemen with diversions to India in Chandragupta and naval action in War Galley. While the scale is not ASL in terms of units size, it is the equivalent in terms of theatres and nationalities. Some modules use somewhat different rules as decided as appropriate by the designer, the basic core ideas remain the same, so while someone who has played SPQR will have to take some initial care with the rules before playing CoF, he/she will not find them all that different. There are a small number of add-ons to main modules, but the vast majority can be played straight from the box. Their Men of Iron series, though a separate line, carry on many of the concepts, albeit in a simpler form, reflective of the simpler tactics.
The second is L'n'L's World at War, which covers a '85 WP vs NATO clash. Though the official back story is a little weird it has no effects on the games. It has quite simple rules, is fast moving and fun, ideal for a change of pace from a heavy ASL scenario. While some modules depend upon others, most, like GBoH can be played on their own straight from the box.
As people will have gathered, my main interest is WW2 and after. Partly that is a generational thing (parents' war, recent history, etc), partly some distaste for the the whole Napoleonic thing, not really sure why. Post school, I developed an interest in history as a side effect from my WW2 interest. So I started from the beginning. I have now worked my way up to GMT's Musket & Pike series, another good game series. Whether I will get to ACW and Napoleon is another matter.
Other good series would be GMT's M&P as mentioned and MMP's PanzerBlitz 2. The latter suffers from being a 1 shot game but there is an East Front module in the works. While there have been a lot of platoon level WW2 games produced, I think it is the best. AP's PG series is much more comprehensive, but a lot slower to play, you have to do a lot more softening up to get anywhere. Because of that it is a lot more realistic, even if the armour model is not as fine grained, but it does come across as a better simulation. For a grand tactical or lower level operational pair of games there is GMT's Roads to Leningrad and Roads to Moscow.
In terms of complexity (1-10)
ASL: 9
GBoH: 5-7, depending upon game.
WaW: 3-5
M&P: 5-6
MoI: 5
PB2: 5
PG: 6-8, partly due to pace and need to master combined arms rather than simply the rules.
RtL/M: 6
The usual caveat of those being my opinions and impressions.
