I am a new project coordinator for a business that has never used one. Is this a good product for us to use or is there something else that I should use first?

In general, this is a good product for project planning. However, as with most solutions, you need to determine your requirements and compare to the available solutions. As far as out of the box solutions, either desktop or on 365, MS Project is very robust. It is also fairly complex and in order to get the most out of it, you will likely need to take some on-line training.

I do not agree with the previous opinion, depending on the implementation, it applies as entry level

Microsoft finally has a true SaaS Cloud offering! This is a brand new product. A stand alone, full featured financial management solution (aka accounting software) hosted and operated by Microsoft.

I think you'll find that Microsoft Project is a phenomenal tool -- but the learning curve to really maximize it is huge. As in, Donald Trump "huge". The software is the king of PM tools, but there is a massive learning curve that you'll need to conquer to use it to the maximum. And, depending on your projects, it can seem like overkill to just "get started" with PM. You said your company was brand new to using PM tools, which makes this a recipe for concern. You need to have a very dedicated direction to using Microsoft Project. I might recommend some 'simpler' PM tools to get things started for your firm..... maybe consider looking at Asana.com as a starting point?