Let's be clear: there are no "new", "revolutionary" lubricant products made for firearms. That's a flat statement, and it's intended to be. All of the lubricants, bases, and additives of suitable use are already well known to the lubricant industry. Specific combinations might be unique, but it's all been tried before - if not necessarily on guns.
Cut to the chase! What should I use?
Let's start with oil. Most people use oils that are way too heavy; thicker is not better! Use a relatively thin oil with the correct properties, and use it very sparingly - most "oil failures" I've seen have been from too much, rather than too little, oil.
Frankly, in terms of mechanical performance, most oils "work"; some are better than others, but everything will make parts move for a while. The weakest area of most oils is in corrosion resistance - and on a gun, corrosion is a bad thing! There have been lots of claims, but those people who have actually taken the time to run experiments to test corrosion on steel have found that the products with the greatest hype are often the worst at corrosion resistance. Not surprisingly, plain mineral oils, such as Rem Oil, score at the very bottom of the list.
If you’re of the persuasion that wants better than a plain mineral oil but still wants cheap and easy availability, there is one product that does pretty well in corrosion resistance (not great, but better than average.) It also has good migration, a fair boundary lubrication package, is the right weight (thickness) for general firearms use, doesn't oxidize over long periods of storage, and is compatible with a wide range of metals and plastics. In addition, it is recommended by at least one real degreed firearms engineer! Just what is this miracle elixir??
Dexron-type Automatic Transmission Fluid (ATF). That's right, plain ol' ATF. The kind you get at every gas station, auto parts store, and even most convenience stores. Synthetic or regular, either will work just fine. ATF is not perfect, however; aside from the aforementioned deficiencies, it does have a slight odor to it, the red dye used to differentiate it from motor oil will stain, and it’s not non-toxic. (If you find those attributes objectionable, a decent alternative that is still readily available is "NyOil." Check your local auto parts store, in the aisle where they keep the miscellaneous lubricants and additives.)