The 75 dollar "basic" phono pre-amp will do an average job with a variety of cartridges. It's settings are not adjustable so each cart is sees will be treated in the same way. The amplitude you get from different cartridges will vary depending on the output voltage of the cart.
The entry level solution will require you to use a moving magnet cart, or a high-output moving coil cart. This should be fine for what you are trying to achieve. The cartridge specs will tell you the output voltage of the cart. 4.5mV would be one of the more powerful models and 1.5 would be on the low side. The output voltage will determine the volume of the turntable in relation to the other source equipment you are using. For instance, with a low output cart the difference in volume levels when switching from phono to CD may be quite a dramatic, but with a 4.5mV output voltage cart, it wont be as drastic.
How esoteric the carts are is not really the point you are interested in. The output voltage is. If you are going for the inexpensive phono pre-amp then you need to stay away from any carts that do not have an output voltage without a number to the left of the decimel point. And in fact, the larger that number to the left is, the better off you will be gain wise.
This is a complex world you are entering, but there are some great sounding value minded carts out there, the GRADO BLACK
comes to mind at 40 bucks. And it outputs 5mV so there would be no volume issues.
Many of the more expensive outboard phono pre-amps allow you to custom tune the pre-amp to match any cart you may be using. Variable load and resistance settings insure the cart is giving you all it can. Probably not useful for you now, but perhaps something to keep in mind as you begin to upgrade later.
By the way, have you considered going with a retro-receiver? Look on E-bay for a vintage Marantz or Pioneer piece that has a built in phono input, or look very closely at this receiver...
The Outlaw Audio RR2150 Retro Receiver
It has a phono input built in. I actually have one of these in my second system and it is kick ass. At 649.00 you get the integrated amp, a receiver AND the phono pre-amp. Look closely at this one, it is highly regarded.
Hope this helps.