It depends on how discriminating you are. Minwax has a few red stains, among them sedona and red mahogany. Look at them on the color chart. Do either of them seem rich enough red for you? If not, you'd need to look at another brand's color chart, or make your way to a store like Woodcraft, where there is a broader range of finishing products. Perhaps the clear deep red you're after can only be obtained with an aniline dye stain.
You may be satisfied with a gloss polyurethane varnish that the big box sells, or you might want a faster-build finish that can be hand rubbed to a very smooth high gloss finish. I'm thinking of Behlens "rock hard table top varnish". It's a very amber-toned varnish that will deepen and yellow the stained color. Again, woodcraft or similar outlet has more specialized varnishes to choose from.
Casey

How true
>It depends on how discriminating you are

Minwax Red Mahogany is singularly high in pigment content and can be problematic.

You have lots of other options besides Minwax. You are unlikely to get any knowledgeable information from the guy/gal wearing an apron at a big box store. (It is, of course, possible, but I'm betting against it.)

Part of the choice depends upon what you are going to use the wood for.

You will only get so much gloss right out of the can. And if you don't have good technique, every flaw will show up in a gloss finish. To get a really super high gloss use hard finish like shellac or lacquer and rub out with finer and finer abrasives. Polyurethane is a poor choice for rubbing. The non-poly varnishes will also work.

Whatever your choice: Run a trial on a sample piece, start to finish, before committing to your project. Several trials might be needed to find one you like.