Can I just buy a bicycle online or is it something you have to get fitted or a feel for? Are there size guides somewhere I can use to measure myself to get the right size for me?
And second side question: i've seen the bicycles they sell periodically at aldi have 'must be assembled by bicycle mechanic' all over the advertising and boxes. Is that true? And does it wipe out the saving?
Yes you can buy them online. Some companies like LeonCycle have their bikes pretty much pre-assembled with minor fixing needed that anyone can do.
Example video: https://www.youtube.com/watch?v=vqt1QE1cG-Y
You can pop into a Decathlon or 99Bikes etc shop to have a look at sizes. They're generally pretty standard and most likely will need a 26" one.
You'll probably want to order from Decathlon anyway to pickup a gel seat cover, side stand, bottle holder and gloves anyway. Cheap addons but well worth it.