I tend to buy everything I can (but see below) and then negotiate for monopolies. A judicious bribe usually does the trick.
Early in the game, the blue, pink and orange properties give the best yields. Later yellow & green. Finally (if you ever get there) red and purple. Brown is mediocre throughout but generates some decent pocket money. If I land on the expensive properties early in the game and I've already got lots of blue/pink/orange then sometimes I skip the expensive properties in favour of getting monopolies and winning by doing a "hotel rush" on those few properties. This is risky (if it flops, the other players have the killer properties for the endgame), but really, the truth is that most players get bored of the game and start doing silly deals and alliances before you get close to the true endgame so it doesn't really matter.
Better not play against you, because that's my strategy, too.
The light blue properties just before jail, and the entire street between jail and free parking. Anything else I buy is trade bait, and I'll gladly trade a more expensive property early in the game in order to get the lower one.
Unless the person is swimming in money, I've been known to actually trade to give a person a monopoly in more expensive properties (after free parking) in order for a monopoly in cheaper properties. If I can get those developed quickly, odds are that person will not accumulate enough cash to properly develop his monopoly.
Other things:
-- You really aren't going to get a good return on houses on any monopoly until you get at least three houses on each property. That's the beauty of the "poor man's" strategy. I can get that magic number on the light blues, light purples, or oranges fairly quickly. The return, especially while the game is still young, can wipe someone out, or keep them from ever developing their own properties to that point.
-- Keep just enough cash on hand to pay the highest rent out there. The rest should be invested as fast as you get it. Get to at least three houses on each property in a monopoly as quickly as possible.
-- Mortgage anything you don't need. The $100 you'll get from a railroad mid-way or late in a game is better than waiting for it to be landed on four times to get that much in return. Even if I have three railroads, I'll mortgage them. The only time I don't is with four.
-- Don't buy utilities. They're a bad long-term investment. If you have them, use them as trade bait.
-- I hardly ever buy Boardwalk or Park Place. The way I figure it, if the game gets to the point where someone gets a monopoly there and develops it beyond a couple of houses each, my strategy has broken down, anyway.
-- I hardly ever mess with the two cheapest properties after GO.
-- When a property goes up for auction, even if you don't want it, always drive the price beyond the mortgaged value. If you can buy it more cheaply than the mortgaged value, do so, even if you don't want it, because you can mortgage it for a proifit. And, it may become trade bait.
-- Adapt. If the expensive properties are the ones that fall into your hands, get them developed as quickly as possible. If you can't afford it, trade down to a cheaper monopoly and get houses on those fast.
We used to play Monopoly a lot while I was growing up. Cut-throat games. And I'd like to think I won more than my share playing the above way. My guess from that experience is the one who gets the most development down the fastest has the best chance of winning. To me, that means focusing on the cheaper properties.
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