The numbers are indeed the amount of data that you can receive per second, and is measured in Mega bits Per Second. (Mbit p/s)
So to watch a streaming video you would need at least 10 Mbit p/s but ideally much more like 50 Mbit p/s as the video can be encode between 3-40 Mbit p/s depending on the resolution and content.
If you also need to download big files, then the Mbit p/s you'll want. On many contracts the upload speed is much lower than the download so look out for that if you need to upload large files.
Of course the more people you have on the connection the more Mbit p/s you'll want.
There are some limitations with the technology used, but most contacts will allow you to upgrade to higher speeds at a price.
Personally I use a 1024 Mbit p/s connection, that is the same for uploading and downloading, these are also known as 1 Gbit p/s (1 Gbit - 1024 Mbits) and pay around £28 a month through Community Fibre. (brilliant)
I would start with at least 150 Mbit p/s provided the supplier can increase it to 500 Mbit p/s or more later, obs depending on cost.
Additional information.
Hard to believe, in 2000 I used to pay £1,250 a month for 2 Mbit P/S, (£2,340 adjusted for inflation)!
If you want to understand a bit more, (at the risk of making everyone's head hurt)
A bit is the basic form of data and can be 1 or 0
A Mbit per second, means you can send 1024 bits every second
8 Bits together are called a Byte,
1024 Bytes are a Mega Byte (MB)
So if you had a photo that was 1MB, it would contain 1024 Bytes that have 8 bits each, so you could say the photo has 8192 bits.
If your connection was only 1Mbit P/S (i.e. 1024 bits per second) it would take 8 seconds to send the file.
Happy surfing!