I hope my answer isn't too lengthy, but here it goes.
There are basically two routes you can go about when choosing cleaning and lubrication products for your gun. You can either
1. Buy individual products, specifically for cleaning and lubrication.
2. Buy a combo product which will do both.
I'll start with combination products. These products can be used to both clean your product, as well as serve as an lubrication. These are handy because it cuts the number of products you own down, and you can usually get everything you need to be done, done, with one bottle.
The most common product in the category is called Breakfree CLP (clp stands for clean/lube/protect). This is an incredibly popular product because it is what is used in the US military, because it is fairly inexpensive, and because it does a fairly decent job at cleanings/lubrication/protection.
Another common multi-use product is Ballistol, which like CLP is used for cleaning/lubrication/protection, and has the added bonus of conditioning wood and leather.
The problem with these products is that while they do a good job at all three tasks, they don't do a "great" job.
Which brings me to my next topic, which is using dedicated solvents (cleaners), and dedicated lubes. Obviously this will bring you a slightly better results because you can pick and choose the best products to fill your needs.
As for solvents, hoppes #9 is by far the most popular, as it is what most people were raised on, as well as what is most commonly found in gun stores, sporting good stores, and just about anywhere that sells gun cleaning supplies. Its a pretty good cleaner.
Other reputable brands would be gun scrubber, mpro-7, they all work pretty well.
As for lubrication, it is my recommendation that you do not use remoil. It actually has very little oil in it, and is mostly kerosene. It just kind of sucks. But they are crazy good at marketing, so that's wy its so popular.
As far as oils go, you have plenty to choose from. More important than the kind of oil you use, is just the proper application.
Hoppes makes an oil, which is lackluster, but works fine. Mpro-7 makes a dedicated oil as well. Militec-one and slip 2000 are high end oils that actually seep into the pores of the metal you are lubricating.
Even a high quality synthetic motor oils works fantastic as a dedicated lube. I've used mobile-1 fully synthetic on everything from my lever gun to my ar-15. Engines get much hotter and dirtier than any firearm.
All in all though, I use CLP for about 80% of all my needs. It works well enough for me, and makes my cleaning kit much simpler.