Linoleum is very hard to find and expensive these days, having been replaced by vinyl flooring which is cheap and commonly available. I suspect you mean vinyl. I would discourage it because vinyl flooring, and especially tiles, are not designed to be safe food handling surfaces. Think bacteria lurking in microscopic crevices, and in the crevices of whatever texture the vinyl has. If you do mean linoleum, it is better than vinyl for a countrrtop.

I would suggest buying Formica that you apply yourself rather than as a preformed counter.

Here is a link that might be useful: Formica for countertops

I have seen that done. I have seen where it looks nice, and seen where it looks awful. The difference is the details- perfectly aligning the tiles and finishing off the edges.

I suggest something different.

We painted our horrible country pink countertops last summer with a special paint made for countertops. It's a temporary fix, but will be fine until we can replace them. They look SO MUCH better!