Hi, welcome to the site.
Have you done any woodturning before?
Is it just wood turning you are aiming to to or other woodworking too?
I personally wouldn't buy new machinery until I knew it was something I was 100% sure on.
It can be a slippery and expensive slope.
If it's just wood tuning you're looking to do, I would go for a cheap 2nd hand lathe to start with.
It will give you the basics and tell you if it's something you would like to continue.
If it's not for you, it's only a small loss.
If it is, you will quickly find the limitations of the machine for your needs and will be able to choose an machine to meet your exact needs when you come to buy a new one.
For instance....
If you only want to turn bowls, you don't need one with a large bed.
If you want to turn large bowls/plates, you will need one with enough bed clearance or one that has a rotating headstock.
12 months ago I had never used a lathe before so I bought a £50 a Record lathe.
I found the clearance to be too low for large turning so I raised the head and tailstock up 3 inches.
I find the bar rails to be a pain when moving the tailstock and tool rest.
I've also found I want to use the tailstock Morse Taper fitting but it's too small.
These are all things I have to consider when I buy my next lathe, things I knew nothing about until I'd owned and used the lathe.
What are you looking to turn? Green wood, seasoned blanks, segmented turnings, spindles etc?
Generally, a table saw is not necessary for your needs.
An electric planer is also not necessary for your needs.
A bandsaw may be useful depending on what you will be turning, but again, not essential.
I personally think it's better to experiment with cheap equipment before committing to an expensive purchase.
But then again, I'm a tight northerner.
Hope this helps.