Great to see some other foreigners are looking Montevideo to live. As a foreigner who lives here for almost 11 years is good to see others coming in, so Montevideo is more rich in culture every year.
I would say the best option in your case would be to live in Pocitos, Punta Carretas or maybe Buceo. These are the regular places where foreigners can live, and have most of the things such as: services, mobility points, works, etc available.
A €500 a month is almost like UY$2,000/month, this in Pocitos at least can probably be enough to rent an apartment on your own (a small one). If you would like a bigger place then yes, probably you will have to share with someone else.
Montevideo is becoming less safe than previous years unfortunately, when I arrived I could go on a walk during night without hesitation, Today, even though it can be done you have to be alert, especially if you are female or elder. Still, it is safer than any other Latin America city, but it's not like Europe or US, where you can go careless chatting on your cell phone while you walk around, you might get your cell phone stolen if you do so.