Pronunciation & Recommendations
I am new to learning German and am hoping to get some perspective on how to approach the process. My biggest concern--as it was for the previous languages I tackled--is the pronunciation, specifically when reading said languages and repeating it aloud. I want to know how others handled this obstacle initially, by either listening to spoken German or relying on the Duolingo lessons in the long run. While on the subject of spoken German, any recommendations for beginner's level podcasts, website, YouTube channel, etc?
Relying on Duolingo is a pretty bad idea considering it has the robotic voice. I'd recommend learning basic phonetics of German. It has an extremely regular and logical system so once you know all the sounds, all the problems should stop. The key thing is to know what sounds (from the IPA) you should hear in what places. Once you're able to differentiate between all those sounds, you can work on anything in any way you want, also through simply listening.
Some of the best phonetics introductions are on this Youtube channel. I really like them and used them a lot. Each one has three parts — consonants, vowels and spelling. Here are the links to the introduction for German: Part 1 — consonants; Part 2 — vowels; Part 3 — spelling;
The great thing about these introductions is that he makes you familiar with the basic IPA (International Phonetic Alphabet) for the language, which is btw one of the most powerful tools in language learning, so it's extremely helpful to know it (not sure if you know it — if you don't you'll learn it there, and if you do, it's even more useful and you can just learn the sounds). They're not too technical or specific (after some time I started to prefer technical Wikipedia articles), but cover roughly all you need to know about basic phonetics and orthography. Also they're pretty brief and concise. If you are learning German, you don't need to learn the whole IPA and all those crazy sounds, just differentiate between those used in German, the ones mentioned in those videos, and there are really few of them. Also the Wikipedia's IPA for... article can be helpful when you want to recap on those sounds and symbols. If you have problems with spelling, once you know the IPA for German, it might be useful to also look at the Orthography article. Recenly I started to find those Orthography articles extremely useful, especially paragraphs like "Grapheme-to-phoneme correspondences" in this one. Good luck :)
Just wanted to add forvo to the list already here. On the website you can search for just about any word (the German part of the site has over 500,000 words) and hear it pronounced by a native speaker. Sometimes you can even hear it spoken by multiple native speakers from different regions.