In my experience, rice quality has a pretty substantial amount of variation, but the cooking device has little to do with it.
While I'm sure that most rice cookers on the market from Japanese firms are optimized and tested for short-grain, japonica rice, I've never had issues cooking basmati or jasmine rice in one, and I've even used them for farro and mixed grains.
I doubt that the rice cooker has much to do with it. I've made rice in heavy cast-iron enamelware on the stove, in a cheap Southeast Asian electric steamer without any fancy "fuzzy logic" electronics, in a fuzzy logic rice cooker, and an mid-range IH rice cooker, which is what we use at home now, and the quality of the rice and its age has a greater impact than the cooking method. I would say that the IH rice cooker produces superior results over our old fuzzy logic cooker, but it's certainly not an order-of-magnitude kind of difference.
Assuming you're located in the US, my benchmark go-to rice brand is "Tamaki Gold", which is from a japonica strain called koshihikari, and I think most of this brand's rice is grown near Sacramento, CA. It's more expensive than the typical Botan or Niko Niko brand calrose rice that's ubiquitious in Japanese supermarkets, but I find the quality far superior, and it's still a good value. My wife tends not to appreciate the Niko Niko or Botan calrose rice very much at all, so we don't eat it at home, but probably 80% of Japanese restaurants in the US are using it or a similar product.
Generally, I'd recommend staying away from the absolute cheapest brands, and choose something that's a couple of notches above. We've used imported rice from Akita or wherever and gotten very nice results, but the differences were far subtler than the price (on the order of $10 vs. $35 for a similar quantity). The sweet spot for quality is near the median price, assuming you're in a shop that offers a wide variety of options.
Edit: Sorry, until your edit, I didn't realize you were working from parboiled or converted rice, I assumed raw rice, as I've never heard of anyone cooking the quick cooking rice products in a rice cooker. (Rice cookers often have their own "quick mode" which shortens cooking time with normal raw rice at the cost of a slightly reduced textural quality). Considering that's what you were starting from, consider using other supermarket brands of rice that meet your target grain size and stickiness/fluffiness, but aren't marketed for speed or convenience.
No noodles are actually called "brown noodles" but the only noodles I'm aware of that are brownish in colour are either wheat or buckwheat.
Given the suggestion to cook it with a "protein source", and given that this is meant to be a quick and easy meal, I'm sure that the idea was to cook some dried noodles briefly in soup along with some sliced or shredded meat. This is common in Asian cuisine, and it can be nutritious, assuming you don't rely on instant noodles and artificial flavour packets.
You'd probably be looking at one of the following:
Ramen, which is traditionally made from la mian (hand-pulled buckwheat noodles, although sometimes they're made from wheat), served in broth, usually with meat and green onions, and often flavoured with soy sauce. Keep in mind that real ramen is actually quite difficult and time-consuming to make, and is not even close to the "instant ramen" you see for 99 cents a package. You can cheat a little and still have a decent meal by buying quality dried noodles and cooking them in real homemade broth, or at least canned broth.
Udon, AKA "thick noodles" (made from wheat), which are also typically prepared in broth, specifically dashi - broth made from kombu (kelp), dried tuna or bonito flakes, and occasionally mushrooms, and seasoned with soy sauce and mirin (rice wine). Meat isn't as common in udon, but fish and tofu are, especially deep-fried. You can still make it with beef or chicken. You can find decent-quality instant dashi at Asian grocery stores, so again, prep time is minimal if you get the right ingredients.
Soba (buckwheat) noodle soup, which (in my experience) is almost always served in miso (again, available in instant form). Seasonings and toppings are otherwise similar to udon, although they tend to get a bit more elaborate. For example, the wiki page references tsukimi soba which means poaching a raw egg in the cooked soup.
Finally Phở, which is the Vietnamese take on this, which uses rice noodles (so definitely not brown). The most common preparation (at least in all of the Vietnamese restaurants around here) is simply the hot soup and noodles with some rare beef dropped in to briefly cook, then topped with basil and bean sprouts just before eating. The broth is really very difficult for non-natives to learn and instant pho is usually terrible, so I wouldn't recommend this for beginners.
Of course you can always just go with good old-fashioned Western chicken noodle soup or chicken soup with rice and vegetables. Chicken noodle soup usually uses egg noodles, which are, again, definitely not brown, so although they're a fine choice, they're almost certainly not what the question is referring to.
Best Answer
Those are fried onions.
They're pretty recognizable, but for confirmation I did a search by image and found this blog post in Finnish containing that exact image. The caption underneath the picture is:
Google Translate translates that to "When the rice is loosened, the onions are added, the -. The third of the leaves for decoration." I think the proper translation is probably something like:
The recipe itself says:
Which translates to (again with a bit of fixing):
(Google Translate thinks "paahdetusta" means roasted, but earlier in the recipe it's pretty clear that the instructions are to fry them.)
You ask about things that look like those but might be smaller. I'd assume they're still onions, just sliced smaller (or possibly shallots) since that's a fairly common garnish. Of course, it's certainly possible you've seen something else; hard to say without a picture of the exact dish you wanted to ask about.