Use the general Simcity 4 strategy: Build slums.
In general the biggest factor that will slow your city's development early on will be money. As money comes from taxes which directly correlates with population you get exponential growth. In order to get to a medium-sized city quickly, it's thus important to spend most of your starting money and income on population, e.g. quantity over quality.
Make sure you spend your initial money on as much population as you can. Use the cheapest sources for utilities (coal power plant, minimal amount of water, drain pipe sewage), and don't buy any services you don't need. One fire dept and no police/education should be enough for the starting city. The only other services that are important as soon as they unlock are garbage and cemetery.
If you've got arable land, I suggest you go with farming industry, as it's not as polluting as regular industry so you can mix it with your residential and commercial, which will save on infrastructure cost. Otherwise, surrounding your coal plant with dirty industry will work okay. You may need two or more sets one-way roads to handle the traffic.
Use a cheap road layout like a grid of 2-lane one-way roads.
Take out all of the loans when they become available, and use the money to fund expansion further. In general their interest rates are much lower than the profit you can make by building stuff from this money.
When high density becomes available, upgrade the center area to it.
This kind of playstyle should quickly net you a slum city of the desired size, which is a good starting point to then build whatever you want using the slums as an income source.