Buying Property
You should always buy any property you can get your hands on, provided you have the money to do so. Some people bypass lesser properties because of its relative lack of value. But even the cheaper properties can provide strong income when equipped with houses and hotels.
Houses/Hotels
As soon as you purchase all properties in a color group, you should buy as many houses as you can afford. You want to begin collecting money from other players as soon as possible. If given a choice, build hotels and houses on your most expensive properties. This maximizes your chance to gain money and become champion.
Jail
Early in the game, avoid jail. If you land in jail, you'll want to pay the fee and get out as soon as possible. This ensures that you won't miss any opportunities to buy the many open properties on the game board. However, late in the game, jail is the complete opposite. Landing in jail can help you avoid paying high rents on owned properties. Stay in as long as possible.
Mortgage
If the game dictates that you must mortgage some property, mortgage properties in which you own only one in a color group. This includes single utilities or railroads. After that, mortgage the cheaper properties you own. Holding on to your expensive properties gives you a chance to earn much-needed money toward the end of the game.