Could you possibly give me a good reason why I should worry about winning a 20k culture game on Monarch?
The following might not apply to you since you don't qualify as a newbie in all respects. I think that for newbies playing such a game helps them to *focus* in on a few aspects of the game. It gives them a focused goal around which to play the game. In Conquests, which I've assumed throughout, it basically implies that one focuses on building wonders and improvements... easy in my opinion than going out and whacking the AIs. You'll probably manage with fewer cities... all the better to learn the trading system when you need it. The game goes rather fast... or at least seems to in comparison to the time I've seen for militaristic games. You do a few things and click "next turn". At least for me, this means I don't feel like I need to get to the next turn... I have plenty of time to check my city for its happiness level (use MapStat or Civ Assist 2), to evaluate options, to micromanage city tiles, micromanage the luxury and science sliders, etc.
With a militaristic game you'll need all that to play it well, but, at least for me, you'll feel more rushed since you've already spent a good chunk of time moving military units, whacking AI units, or watching your units get whacked. Since you don't feel rushed, you might also more naturally feel inclined to actually read the civilopedia on what improvements do or what units do, or read an article here. Maybe not Monarch, maybe lower... that's not really the point... but a 20k on Monarch I really think such easy enough. Plus, if you win it on Monarch you'll have the confidence that you won when the AI had extra units and a better production rate... not something you'll get on Regent.
The biggest point here comes as that the 20k more easily creates a focused sort of game, at least in my mind, than any other game. Everything *revolves* around one city in a 20k game. You can pretty much mismanage the rest of the empire, as long as your 20k city does its job well enough and you get your techs on time (not too much to worry about until after Education here with a 20k game). You have to fully manage your entire empire in other types of games... that requires more attention. And when you don't know the game, that can imply information overload, or enough information at once that it seems more stressful than relaxing and fun. OCC 20k games use to take me 2-4 hours. Since I play a little more carefully now, something like 4-6 I'd say. Regular, peaceful, non-militaristic (as few wars as possible basically... maybe a GA war... maybe) 20k games probably something like 10-15 hours... for the whole game.
Better yet, why I should worry about seeing how high I should get in general?
Maybe you'd find the game more interesting or more fun that way. Maybe not. By all means suit yourself.
P.S. In real life, I've also never burned a city down and carted off the survivors as slaves, so my Hitler credentials are decidedly lacking.
Oh... lacking credentials? And you dared to walk into my office and apply for THIS job? Get out... now.
I certainly don't view civ III as some sort historical simulation... or at least not to the degree timerover51 does.