Peat varies in quality depending on where you get it; some is quite earthy. Generally it’s a poor fuel for a stove, it glows nicely and gives off pretty sparks but isn’t dense so doesn’t last very long. I’ve been told it burns very tarry and is not very good for your flue. However it does smell gorgeous when you allow some smoke into the room or you go outside. The tiny amount you will burn is insignificant compared to what gets spread on gardens or burned in peat-fired generating stations.
Coal is a bad idea for a multi-fuel stove as with enough draft it can burn white hot, which can melt the cast iron grate and baffle plate. Some coal is very tarry.
Smokeless fuel is fine in a multi-fuel, it will glow nicely and cleanly all evening and most of the night and forms a good bed for your logs.
For logs you need a good hot bed of embers, either wood or smokeless, to achieve a hot enough temperature so that they glow right through and don’t smoulder and produce tarry smoke. Well-seasoned logs will burn hot and dry and look nice.
Best advice we were given was to err on the side of a smaller stove, which you will be burning harder and thence hotter and cleaner.