How would you show superlatives in sumerian (i.e best, greatest, tastiest, warmest, etc.)? Would there be a suffix to add onto the root word to show that it's the "best/most" of something?
Hello! This answer is, as with many things in Sumerian, more complicated than you might expect. The first part of the answer is that the Sumerians did this kind of superlative structure very rarely, especially in contrast to constructions of equality, which they used really often.
In fact, there's a whole case ending, called the equative, that is used just to compare two things as similar or equal - the case ending is -gin, and is best translated as "like, as, similar to." A simple sentence structure is "X Y-gin [verb]", where the verb has an adjectival meaning (like gal "to be big"). So, Ur egin gal "The dog (ur) is big (gal) like a house (e)", i.e. "The dog is as big as a house".
A rarer structure is comparison, corresponding to "more [adjective]" or "[adjective]-er" in English. Sumerian, like some other world languages, has a specific verb used for this, dirig "to exceed". So rather than saying "X is bigger than Y", you'd say "X exceeds Y as to its bigness" - "[X] + [nominalized adjectival verb with possessive suffix] + [Y in the locative or dative case] + dirig [conjugated transitively]". (Note that Y is in the locative case if it's an object and the dative if it's a person.) So, Ur namgalabi ea ibdirige "The dog (ur) exceeds (ibdirige) a house (e with locative case -a) as to its (-abi) bigness (namgal)," i.e. "The dog is bigger than a house."
And finally, superlatives, the "best, most, -est" structure. There is, in fact, no literal way to convey a superlative in Sumerian, and so the easiest way to translate this is to reframe it away from the superlative: "My dog is the biggest!" would be more naturally expressed as "My dog is bigger than those dogs!" (Urngu namgalabi ururbia ibdirige) or just "My dog is big!" (Urngu gal).
There is a structure that can be translated as a superlative, which is "X + [past participle of adjectival verb] + [possessive ending]": Ur galabi "the dog, its having been big...", which can be interpreted as "the biggest dog". But it's used very rarely and can be ambiguous in translation (Ur galabi tur "The dog, having (formerly) been big, shrank" doesn't imply the dog was the biggest at any point).
These structures can be super unintuitive for English speakers, so if you have a specific example to translate, let me know!