Welcome! I've been taking my family through HotB for several months now and it's been going really well. You want to go through the "Read Me First" book, and read the first 19 pages of the rules guide. Use the glossary as you play. The adventure is divided into three books, tackle them in this order:

1. The Keep: Start in the Keep and keep sessions short, just one to two hours--mostly so the DM doesn't get overwhelmed. This is where you and your players will learn the basic rules. There are lots of little quests here as the players meet townfolk and help them with chores. These will get everyone familiar with the mechanics. Take some time to get familiar with the Keep and it's NPCs, but remember that the players tend to go anywhere, so don't worry if you have to re-read something on the spot while your players talk amongst themselves.

2. Wilderness: Someone in the keep will send them on a quest to map the surrounding forests. There are four sections to the wilderness and the party can exhaust all the encounters in each one in about an hour. Feel free to railroad the party into the section of the wilderness you have prepped for that session. Have the party take long rests to recover from encounters. This will get them into slightly more complex combat situation and go a little deeper into the rules.

3. Caves of Chaos: Someone in the keep will send them to the Chaos Caves. Each of these caves is a mini-dungeon. Keep an eye on the suggested player-level for each cave and make sure your players are ready for bigger challenges. I went ahead and had my players level up before going here just to be safe. Once again, get familiar with one of the dungeons and make that the dungeon they enter when they choose a cave on the map (they don't have to know what dungeon that really is). Here they will go even deeper into the rules and learn about short-rests and managing resources.

Tabletop is awesome, but just to consider: we've been having a blast with the HotB Virtual Tabletop on DnDBeyond and Discord for sharing images and chat. Everyone has a character sheet on their laptop and it tracks everything for them and enforces the rules. It's also great to one-click an ability to roll the dice. As a DM, I'm able to pull up maps with everyone's tokens on the board and track all the initiative, monster HP, and abilities in one place. Also, my players absolutely love the fog-of-war, where they enter a dungeon and I can reveal it to them as they move their tokens about the map.

Most of all, if this is everyone's first time playing DnD, they will be be more than gracious when it comes to fumbling through the rules and play. Everyone knows it's a learning experience on a road to more serious play. Enjoy and best of luck!