There is a lot of content I want to pull directly from other websites, particularly Reddit. I know people condone reposting other IG photos as long as credit is given, though I haven’t been able to find any etiquette in regards to posting from other websites. How should I go about doing this?
You should always give credit where credit is due. Also, posting images depends on what image you are trying to repost. If you are reposting images that are coming from artists, then they will naturally react about their image getting stolen but if you are just reposting memes or random images from the web then there’s really nothing to worry about that.
Keep safe always though and give credits. 
Is there a certain way to give credit? For instance, would ‘Credit: [name of photographer]’ be okay?
Yes, that’s the right way to credit the owner or link the original post. Also, giving credit is not enough if the there’s an owner of the photo because you will sometimes have to contact them and ask permission if you want to use their image.
Having said all of that. I am using images found on google or extract images from other accounts without asking for permission. Do what makes you feel comfortable but it’s better to stay safe.