Your cabinet is designed to accept the very quiet signal from a guitar pickup. Instead you are sending it the line-level signal from your pedal.
Your cabinet is designed to add colour to a clean signal. Instead you are sending it a signal that already has all the colour and tone you want.
Assuming you definitely want to use your pedal, the ideal would be to use an amp which doesn't add colour, and accurately reproduces the signal it is given. The best thing for that is to use a PA amp, a keyboard amp, or just a hi-fi.
To make the best of the guitar amp you already own, you need to make it distort as little as possible, and you need to prevent the pedal from overdriving it:
- if there is a choice of "active" or "passive" channel, use "active". This is designed for active pickups, which output a louder signal.
- turn the gain know low, and adjust volume with the other knob.
- turn the output volume of your pedal down low
Those professionals who use amp simulators generally connect them direct to a mixer, which will route the signal to monitors, PA, recording input etc.
"PA amp", "keyboard amp", and "hi-fi" are all words used to describe an amplifier and speakers which aims to have a full frequency range, and aims to accurately amplify the input signal without distortion. Anything marketed using these terms is likely to do the job well -- your main choice is size and power. Purely for home use, a small, low power system will do the job well. If you want to compete with someone else's guitar amp you'll need something bigger and louder. If you want to gig, you'll need something bigger again (or jack into the venue's PA).
You might imagine that plugging your multi-FX pedal into a hi-fi would be a second-class option. However this isn't the case. A hi-fi (by which I mean the kind of amplifier you'd plug a CD player into) is designed for exactly this kind of signal. Many multi-FX pedals have a stereo output. Using a keyboard amp or a single-cabinet PA combo, you don't get the advantage of the stereo output. Plugging into a stereo PA, or a hi-fi, gives you stereo sound, making the best of effects like room modelling reverb, stereo ping-pong delay, stereo chorus, and so on.