First and Foremost- Celebrate!! Celebrate with your partner, your family and friends. It is easy to get swept up into wedding planning so quickly, but enjoy engaged life for a little bit first. Understand that you just made a huge commitment together, and although its not "marriage" it is just as important :)
Once you're all celebrated being newly engaged, out, start thinking about where you want to get married, prioritize your ideas in a category, for example: if location is important, choose that location, if type or size of venue is important find venues in that category, or if you are looking at a destination wedding, research what goes into destination weddings first :)
Now, you have a venue in mind, I would always have 2-3 backups (this goes for any vendor), but you never know what could happen when you actually visit the venue! For us personally, we went to visit a venue I thought for sure would be "our venue" and when we went I realized it was nothing like how it was advertised. If you can't visit your potential venue, ask if the venue will do a virtual tour.
So lets chat vendors! Now we have the perfect venue, our next step is prioritizing vendors! Your top booking vendors may be different than someone elses, but what ever category of vendor is most important to you-start there. Pick 2-3 of your favorite vendors in that category and reach out to them first, if none of them are available, then move on to your next 2-3. The biggest advice I have for you, is stick within your budget. If you see that a photographers starting prices are $2,000 more than your top end budget and you are not willing to budge, the photographer most likely is not going to go down to your price. So be realistic in your choices, and do your research before you reach out to your vendors :)
If your vendors have inquiry forms, be specific on them! I know it takes a little more time on your behalf, but it helps your vendors get to know you better and make sure that you have the perfect fit for each of your needs!
Most importantly out of anything, don't rush the process unless you have too. Take your time making decisions and investments, because weddings aren't cheap, and you want to make sure you're making the best decisions for you and your partner!