Bible Gateway is usually the first I go on the internet to start researching a piece of Scripture. They have some of the best and easiest-to-use tools on the internet. You should know that the lion's share of those tools are behind a $40/year fee. On the one hand, no one likes to spend money. On the other hand, just one of my favorite resources on Bible Gateway would cost me $319 if I bought it outright. Bible Gateway Plus is honestly one of the most no-brainer purchasing decisions as someone who loves to research Scripture.
To get to the resources, look up a passage and click Study. For today's example, I'm going to use Luke 1:26 ("In the sixth month of Elizabeth’s pregnancy, God sent the angel Gabriel to Nazareth, a town in Galilee").
Most of the resources listed will be labeled "Plus," which you have to pay for. And, to be honest, most of the free resources aren't that helpful. But a few are.
Encyclopedia of the Bible (free)
This resource gives a well-resourced encyclopedia on whatever keywords show up in the chapter or are related to what you're looking at. For Luke 1:26, 21 encyclopedia entries are listed, including Angel, Annunciation, Elizabeth, Gabriel, Immaculate Conception, Nazareth, Virgin Birth, and more. On the article "Gabriel", I learn about his showing up in the book of Daniel, the meaning of his name, and where he shows up in literature outside the Christian Bible.
The IVP New Testament Commentary Series (free)
This commentary gives brief, non-technical entries for the passage at hand. Here I learn about the Jewish process of betrothal and marriage ("The initial phase, the betrothal, involved a formal, witnessed agreement to marry and the giving of a bridal price. At this point the bride legally became the groom's and could be called his wife. About a year later the actual marriage followed").
The NIV Application Commentary (some are free)
This series gives both thoroughly background and theological information, as well as—no surprise—a big emphasis on applying the passage to today. It's not available for free for Luke, but it is for Genesis. I believe its availability shifts around based on deals with the publisher.
NIV or NRSV Cultural Backgrounds Study Bible (paid)
I actually own a physical version of this and it by far my favorite and most-recommended study Bible. If you don't want to spend the $40 on Bible Gateway Plus, then spend the $26 to own this Bible. It is chock-full of charts, pictures, and notes to help the Scriptures come alive. There are 65 notes on Luke chapter 1 alone.
Zondervan Illustrated Bible Background Commentary (paid)
While the above is my favorite study Bible, the Illustrated Background Commentary is my favorite resource. If you were own the physical volume, it would be 10-volumes of full-color maps, charts, images, and of course entries on every chapter of Scripture. It's intense.
On Luke 1:26, we find out that Nazareth is never mentioned in the Old Testament or 1st century Jewish writings. But its existence was archeologically confirmed in 1962 by an inscription in the city of Caesarea Maritima.
If you want to dip your toe into language studies, Blue Letter Bible is a good, free place to begin. In our case, I type in our reference (Luke 1:26) and chose the NASB translation (which is the most word-for-word translation available). Once I'm taken there, I click on tools and it shows me the Greek text up top, as well as what Greek word is being translated by which English word.
You will see a column called "Strong's" and then each Greek word will have a number next to it. Strong's Numbers is a system of organizing Greek Words for easy lookup. So, I can click on G32 for the Greek word
ἄγγελος. That takes me to a lexicon page with a basic and longer definitions, and all the uses of it in the New Testament. This is a great way to do a specific word study, or to define an unfamiliar word.
If you want to watch instead of read, there's tons of great resources out there as well.
The Bible Project is my favorite video resource, an incredible library of animated and interesting videos. They have series on the entire narrative of Scripture, how to read the Bible, and book-specific videos as well. I can search for Luke 1 and find an 8-minute overview of Luke 1-9. That just scratches the surface of what they have available, which includes word studies, theme studies, and more.
Third Mill has a large library of videos about Scripture, theology, and ministry. There website is intended for classroom use, so it also includes study guides, lecture manuscripts, and discussion forums.
Biblical Training, led by possibly the greatest biblical language scholar alive today Bill Mounce, has a massive library of courses about Scripture, theology, and ministry, all for free. They include beginner, undergrad, and graduate level courses that will stretch your mind and faith.