First of all, congratulations on your new recording and on taking the steps to ensure this is a successful release! There's a few things you'll want to do to ensure your new album gets the exposure it deserves.
The first step is to take a look at your social media and make sure it's in top shape. This means that you're posting regularly (several times a week) and posting engaging content. (Think of the 70-20-10 rule). If you don't have a strong audience, then no amount of team members or promotion will be able to help you. This is why it really does start with your social media and tending to it as you would a garden. The more you nurture it, the more room it has to grow. Abandon it and well, the results are pretty grim. If you need help getting your social media in shape consider hiring a digital marketer or publicist to help you with this. Many publicists and digital marketers offer these services.
Next you'll want to think about a team. You say you've recorded the album so I'm not entirely sure what you mean by "a professional recording" or why you'd need a producer (usually the producer is part of the recording process, so if that's done, you shouldn't need one.) Though you may be thinking of mastering if you haven't already. A manager isn't really necessary until there's actually something to manage, so skip them as well. What you will need is a publicist to promote the release—publicists start album/EP campaigns 8-weeks ahead of release and need the mastered tracks, promo photos, and a strong bio to start, so make sure you leave yourself plenty of lead time. You'll also want to consider booking a release show, and whatever you do, make it an experience. All live shows should be memorable, but your release show especially should have something special going on, something memorable.
In fact, take that thought process with you in everything you do: if it's not memorable if it's not adding value to your fan's lives, consider reworking it. The goal with your music is to truly connect with your audience.
Best of luck!