Looking at the products, Chestnut's melamine lacquer looks like it can be used as its own base coat, although they say it will also go over a base of cellulose lacquer. Whilst the technical information says it can be applied by brush, cloth, roller or spray I strongly suspect the first three options only really apply to small items because the stuff is reckoned to be touch dry in five minutes. That would lead me to suspect the best application method for a large surface, such as a table top, would be a spray gun.
The acrylic lacquer has a longer touch dry time, about twenty minutes, so I suspect you might be able to apply it satisfactorily with a roller or foam brush. Again, this product can be used as its own sealer, although you can use acrylic sanding sealer or cellulose sanding sealer to help build up an initial coat thickness.
Neither of these products suggest using shellac as a sealer or base coat, and I wouldn't use it either, unless, as I said before, you are aware of specific potential adhesion problems such as contaminants. Even if I was aware of such problems and I chose to use a shellac as a barrier coat because of its well known qualities for both adhesion and to use as a universal base coat under other film forming finishes, I would only ever use dewaxed shellac for this purpose. The reason being that dewaxed shellac is the only form of shellac over which just about any other film forming polish type will adhere to satisfactorily. Water based finishes are sensitive to shellac with wax in it.
On the whole, even though shellac has a great reputation as a universal sealer and base coat, I don't recommend using it unless there are specific problems that might cause the first coat of other finishes to fail. Generally, it's best to stick to the finishing procedures recommended by the manufacturer of a particular product, unless you really know what you're doing. Slainte.