I was doing lighting on a small scale about 12 years ago, just prior to the LED disruption. I ran a 24-channel DMX controller and various traditional theater/stage lights as well as a couple of DJ type motion gobo things. I can't give you advice from current experience, but based on the limited knowledge I have of the entry-level scene nowadays, I could make a few comments and perhaps get feedback from those more knowledgeable.
"PAR" cans are probably the most popular style of light but not the most useful. PAR stands for Parabolic Aluminized Reflector, which is a type of bulb -- basically a spotlight or floodlight style bulb. The traditional incandescent PAR bulbs fit into cylindrical cans. They're typically used to flood the stage with light. The beam angle and pattern is a function of the lens built into the bulb and they tend to have soft edges. Gel filters were used to get various colors.
With the advent of LED, we struggled for a while to get the right combination of phosphors for the color temperature and color rendering index (CRI) that was appealing. Inexpensive "white" leds were poor quality for a while. Then RGB arrays became a popular low-cost solution. They immediately gave remote control of a wide variety of colors (previously one would have to hang separate PAR cans with gel, and blues especially were weak). But with the RGB arrays, "white" still looked too "cool" (color temperature wise). Nowadays, the RGBA (red, green, blue, amber) arrays are probably the best choice for a low-cost solution. You can get all the colors, and a decent white.
LED fixtures with RGBA arrays that take the place of traditional PAR cans are probably the most popular low-cost fixture, but ellipsoidal or fresnel fixtures might be more useful. The problem is they cost more. The big advantages of ellipsoidals is you can focus and crop them. They tend to have sharp edges, and a long throw. Fresnels have a shorter throw. Their advantage is they have soft edges that blend easily.
I'm not an expert, more of a hack than anything. But if I were working on a large scale with longer distances, more fixtures, and complex scenes, I would want a lot of ellipsoidals. But on the smaller scale that's more fitting you or me, I might only want one or two. An ellipsoidal is perfect for highlighting a killer drum set. You can focus a lot of light on it and control the edges so it doesn't spill into video screens or back stage junk. They're also good for other spot areas that don't move -- keyboards or a player/singer that doesn't move around a lot.
On the smaller scale end of things, I'd probably find fresnels the most useful. I can keep adding more and they just blend nicely. I can focus and crop the light where I need it, but I know I won't have harsh edges.
The LED version of "PAR" are probably the least expensive fixtures and therefore they tend to be the most purchased. They're fine for mostly uncontrolled wash and uplighting. They'll definitely give you some color compared to having nothing.
I agree that software is going to be a better bet than trying to do everything on an expensive hardware-based dmx controller. Some of the cheap stuff has IR or microwave wireless control. You can link fixtures into groups and use a handheld remote to change colors and dim. That route is great for a low budget if the fixtures will also work with DMX so you can include them in your inventory once you add the dmx boxes and interface to a laptop or something.