Mats are great for providing cushion under your joints, designating a personal space to practice and for creating traction for your hands and feet to prevent slipping.
There are many choices with different materials and thicknesses. Basic mats are inexpensive but need replaced more often. My favorite mat is Liforme as it's eco-friendly, non-slip and has great alignment markers.
Yoga blocks are a great tool for helping with deepening, supporting, helping with alignment & accessibility in poses. They're also relatively affordable!
Blocks can vary in weight and stability: FOAM: Lightweight, but not as sturdy. Great for travel and restorative practice. CORK: Heavier, but more stable. Great for standing poses & under hands,. Ideal for home practice.
Yoga straps are really useful for improving flexibility, increase strength and allow you to modify poses. They essentally act as an extender to give more length in many yoga poses.
The following products aren't a must, but can be a great addition to a yoga practice.
Yoga wheels are a fun addition to a practice and wonderful for helping open up the chest/back and for creating strength movements.
Yoga towels can be super useful during a sweaty vinyasa practice to avoid slipping, sliding and wiping away sweat.
Keep your mat clean and store all your props, keys, cleaner, keys and more in the yoga bag! The Manduka is hands-down my favorite!