Hi Paul,
Although I would agree with David's comment about collecting as much of the dust at source, most of these twin bag chip and dust extractors only use a cloth bag as the filter, so fine dust gets back into the workshop. You can get fine filters for these extractors but they are quite expensive. Alternatively, if practical, site the extractor outside the workshop, where dust that passes through will not be a problem.
On that basis, I would go for the Air Filter and locate it near the lathe. You will be surprised how effective this type of recirculatory filters can be. But I would use a cheap vacuum cleaner to provide localised extraction and still wear a mask when sanding.
Ideally have both the twin bag extractor and the filter, but I appreciate cost is a significant factor for everyone.
One idea, for saving money, if you do go for a twin bag extractor, I use ventilation ducting (from Screwfix and other suppliers) for my dust extaction system. I have rectangular box section across the roof of my workshop and the flexible PVC pipe for local connections to the extractor and the lathe hood. Yes, this stuff IS flimsier than 'proper' dust extraction accessories but it is also MUCH cheaper. And before anyone says the flexible hose won't last - one 3m section behind my lathe (cost £3.99) is just over five years old, with only one piece of gaffer tape to patch a hole!