Like always the results depend on what you are trying to accomplish with the new equipment. So in our hypothetical example let's say we want an all-around studio mic that can produce crisp, clear sounds. We also want a preamp that can provide a good signal to noise ratio and does dirty the signal. So what's the answer? Well in short, you want to spend more on the preamp than on the microphone. There are exceptions to this, so let's dive a little deeper into the reasoning behind these answers.
The microphone comes first in the signal chain, and is the first thing that captures the source. So it is important to have a good quality microphone that properly captures the source content and its nuances. However, plugging a $2,000 microphone into a $200 preamp will degrade the quality of the signal. A cheap preamp is more likely to add noise to your signal and even shave off some of the harmonic content through signal loss. It may also yield a flat, dull sound. So what's the point of having such a great microphone if the signal is getting destroyed by a cheap preamp? If you haven't figured it out yet, the goal is to find a nice balance between the two costs that fits your own needs. This doesn't necessarily mean to split your budget and spend half on the mic and half on the preamp; although it could be a good place to start.
When researching microphone and preamp options carefully read reviews and look at popular combinations that people are already using. If you are looking to pair a microphone with an interface with multiple mic preamps, then read the specifications to check the quality of those preamps. There are many great microphones that fall into the affordable range. Purchasing one of those will leave you with enough to buy a decent preamp to pair it with. This will give you a killer combo to capture some great sounds. Just remember that the preamp is more important, but don't let the cost gap between the too get too big. A great preamp won't make a crappy mic worse, but it won't necessarily make it better either. I bad preamp will almost always make a good mic worse. Do your research, read the reviews, and compare various combinations until you find a good balance of cost to quality.