I've heard that the best method for sustained metabolism and muscle gain is proportioning your day into six small meals. My question is what are the suggested/best/cheapest foods for those meals, besides some sort of protein? What is the easiest way to get these meals in?
Do you want to gain weight or do you want to gain muscle?
The cheapest way to gain weight, mostly fat is by consuming lots of carbs like sugar, high-fructose syrup etc.
Considering, most (all?) people want to gain muscle, you should be more careful:
Don't try to force weight gain too much, remember you want to look good, not fat.
Cheapest foods are hard to answer, as food prices vary widely from location to location.
The most important thing for you to figure out what the best foods are is to keep a food journal when you try various foods and see how you feel after. Avoid the foods that make you feel fatigued/have diarrhea/unusually achy/anything unpleasant, even if someone else says it's really good for you.
If you have a particular health problem or tendency towards one (perhaps problems closely related family members have), starting with a selection of foods designed to help that issue is the best idea. And this is where it gets really hard to recommend - someone with IBS would be best served eating ripe bananas, but someone with blood sugar issues should avoid eating bananas, and if they do they should be under-ripe.
Something you can consider is pesticides, which are harmful to everyone, and should inform whether you buy certain foods organic or non-organic. A lot of pesticides aren't water soluble, so washing your food doesn't help either. Some foods you should only eat organic versions of are; peaches, apples, bell peppers, celery, nectarines, strawberries, cherries, lettuce, grapes, pears, spinach and potatoes. Of course buying organic increases the price, but there are non-organic foods that don't have a high risk of pesticides (bananas for instance, assuming they don't cause you problems otherwise).
For meats, red meat gets a bad rap, and in some ways it's deserved, and in other ways not. Grain fed beef is one of the worst foods you could possibly eat, but grass fed beef is quite healthy and one of the best sources of protein you can get. Grass fed beef is a lot more expensive though, so unless you're lucky you might be better off following conventional advice and sticking to chicken and turkey. Both chickens and turkeys can eat pretty much anything, so the problems of feeding cows grain doesn't come up with the birds. I prefer turkey simply because it's less common, and therefore less likely to be overproduced, so the quality will be better.
With fish, thanks to Fukushima, recommendations end up depending on whether you live near the Pacific or Atlantic, or if you're land locked. If you're land locked, I'd say just skip eating fish entirely and get some fish oil (it's expensive, but pretty nutrient dense, so worth getting even if you're on a tight budget), unless there's local freshwater fish you can buy. If you're near the Atlantic, stick to small fish with short life spans that are local. If you're near the Pacific, you might be best following the land locked advice as well, or research local fish farms to see what quality they produce.
For carbs, wheat is often a problem for people, so it's a pretty safe bet to avoid it and go for barley or rye instead. It also is a good idea to avoid corn (maize), GMO foods have been shown to cause some pretty serious illness in animals, so it's possible that's happening with humans as well, and it's pretty much impossible to buy corn that you're certain is GMO free.
The easiest way to get foods will also depend, I've seen some people who have no trouble making themselves a lunch box to eat every day, and those people would eat the same type of meal throughout the day. I find that tedious, so I prefer to go for smoothies.