(Don't get me wrong, I also love new shiny new equipment!), Every company will have pages and evidence why their new thingamagig is better than the other one, and this can be very overwhelming.
Personally, I'm a minimalist. When I first started teaching bootcamps, we used zero equipment other than a Yoga mat. This was challenging for me at first, but it was incredibly eye-opening. There's just so much you can do with just your own bodyweight. You really don't need a lot.
Here's what I recommend all of my online clients purchase before we start training:
1- A Yoga Mat
Or something that's grippy and can provide support. A beach towel is fine for outdoor workouts as well. Most of us only need about a mat's width of space for a great workout, so good news for small spaces!
Bands, medicine balls, a couple dumbbells, or a suspension trainer like a TRX are all great. I prefer my clients have at least one heavy weight and a set of medium/ smaller weights or bands. That could be a 10lb medicine ball, a medium/light band or a jug of water and soup cans.
If you are pregnant, postpartum, or breastfeeding, this is critical. Always keep water nearby so you can stay hydrated during your workouts!
If you're starting out, invest in something that feels a little "too heavy" to work towards and some more "manageable" bands or weights to work with. Generally when I work with clients we use a combination of body-weight exercises and whatever resistance they already have and add more when it's necessary.
If you want to truly make this a functional space, make sure you have at least the length of a yoga mat. Natural light, a giant mirror so you can see your form, a basket to hold all your equipment, some room spray, and a stopwatch, are all helpful as well.
Need ideas on what workouts are safest and most effective (and how to get them actually done) for postpartum?