Introduction to the Sicilian I am trying to work on my openings and start playing the Sicilian as a response to 1. e4 but I am slightly overwhelmed by the huge amounts of resources available. I am rated around 1850 FIDE and I mainly play the French as a response to 1. e4 and the Gruenfeld as a response to 1. d4.

What would be a good resource for a player of my level to get used to the Sicilian? My goal is not to get an extensive knowledge of the opening, I just want to play/become familiar with a few variations, i.e. the Najdorf, the Sveshnikov and the 3. Bb5+ variation after d6
There's no known recipe that works for everyone for how to approach the Sicilian (or any new opening) as a newcomer to the opening, but it definitely helps if you concretize your target even more than what you've described in the OP. To do that, you might find the following general considerations helpful, specially given that Sicilian is a vast and rich system in opening theory:

Mindset and approach:


Find players whose approach to employing the Sicilian suits your style, in terms of: the type of play (closed, open, sharp), depth of needed theory, whether it's midgame or endgame oriented etc, and study their games (e.g. Kasparov's games). 
When studying such games, for at least the first 10 moves, constantly ask yourself what the purpose of each move is in theory (for the move order you're trying to learn), and if you find the point of a move goes over your head, follow through a few variations with the engine with and without that move and see what repercussions it has on the ensuing variations.
Even more important than understanding specific moves, try to learn what the underlying plan of the particular Sicilian variation you're studying is, this really cannot be emphasized enough. Once you know what the line aims to achieve from a strategic point of view (e.g. is it to create an isolated pawn structure, is it to establish a permanent knight post in the centre, is it to trade bishops or keep bishop pair, etc), making sense of the moves and the ensuing play becomes much easier to grasp.
Once your particular type of Sicilian system (Kan, Sveshnikov, Dragon, Taimanov, etc) is decided, then you can focus your resources on that system and your search becomes much more meaningful.
Once you get a grip of the basic ideas behind the system of choice, start carving your own version of the system, personalize it according to the kinds of positions you feel comfortable playing and where your skills lie (middlegame, tactical, strategic, endgame player etc), and in that regard learn the relevant transpositions, while always checking your new ideas with an engine.
Keep practicing your developed system, 1-2 two blitz games won't cut it, you need to play many many games until the concepts start to sink in and you form a good intuition for the opening. Keep analysing each game irrespective of the outcome, go back to the opening stage and find improvements.
A training exercise that is often quite helpful is to: play the opening lines you're trying to master in your head without any visual aid (board, phone) against yourself, e.g. when on a commute or during a nice walk. When playing blindfolded against yourself, saying the moves helps a lot to remember the position (that is, literally saying to yourself Nc3, d5, etc).


Tools for the learning process:


To keep a clear note of the ideas you learn along the way for each line and move order, create a study on lichess and fill it up with annotations and arrows, and go over these studies to review and brush up on what you've learnt every now and then. 
Similarly, create a study for the personalized system you start building for yourself. These studies can be made private, and of course they will always be work in progress as you will regularly update them with any new finding. For more on lichess studies see also this post.
To explore opening lines and try new ideas, use the opening explorer on lichess (and many other available ones online) with the Stockfish cloud engine active in the background, play through the lines and cross check your ideas with the engine.
There exists various video series on the Sicilian, e.g. on chess24 see here (for instance the Taimanov one by Robin van Kampen has become quite well reviewed).
Other online resources: Check out the content on various chess youtube channels, e.g. ChessExplained or ChessNetwork, they provide very clear commentary as they play or analyse games, and they both frequently play the Sicilian too. And of course the wonderful lectures by Yasser Seirawan, e.g. on the Pin variation or the Accelerated Dragon.
Last but not least, books, books, books! They still remain the best resources in chess. There are plenty written on the Sicilian too (e.g. see the recommendations by Chris), find one author and book level that matches your taste and get started! Reading chess books is almost always an interactive process, where either you're pausing to calculate something blindfolded, or setting up a board and going through some variation discussed in the book. Generally, they're not read cover to cover, and specially if they are extensively covering something, such as Endgames in chess, or Pawn structures, you will be jumping around the book frequently to read up on the bits that currently are relevant for your improvement. Remember that there's no one book that is the best, these things are always subjective to our preferences, so try to explore and find one that you like and read up patiently ;)