Should I learn Chinese first and then Korean, or vice versa?
I have learned these two languages and I find Korean easier than Chinese.
I am Vietnamese and the language is heavily borrowed from Chinese. Korean and Japanese also have Chinese roots. That's why it's easier for me to speak Chinese, but writing is not the case, it's very difficult. In contrast, Korean has a harder way of speaking and grammar but is easier to write. Hangul Korean alphabet can be memorized in a few hours.
Don't know your mother tongue but for ountries with languages that are not related to Chinese, I recommend learning Korean first because it is easier. Learning 2 languages is easy to confuse. Or you can choose to study in advance for the language you prefer.
I tend to connect Korean and Chinese words with Vietnamese words to remember longer or imagine similar words, compound words.
For online apps to learn vocabulary, I used Hanzii Chinese dictionary for Chinese and Naver dictionary for Korean. Highly recommend Hanzii dict because it has different features and works like a package.
These 2 dictionaries when searching for words, they will suggest similar words with examples and reading so it is very good for this learning method.