The perennial sweet peas will be the fastest if you buy established plants - depending on their size / age. If you grow them from seed (which is cheaper and easy access - you should be able to get seed at hardware shops like B&Q or The Range or garden centres) they'll take a year or so to get going. Established plants should give you a reasonable screen in their first year after planting but you'll be getting a decent screen by 2028.
The roses - if you planted them this winter, they should be providing good screening by summer 2028.
The honeysuckle is vigorous and if you planted it this winter or coming spring, you should get reasonable coverage by the summer and abundant coverage by summer 2028. The honeysuckle would be good because (a) you can chop it back hard if it gets out of control (b) it smells wonderful (c) it's usually affordable (d) wildlife like it.
A quick solution could be:
You could mix and match the trellises and obelisks to create depth and interest for both you and neighbour.
For example, you could have 3 upright trellises, about 20cm away from the fence, and spaced evenly along the fence line. Up these you could grow roses and honeysuckle as they smell lovey and would be pleasant for your neighbour. These should be giving good screening by summer 2028.
Then in the gaps between the trellises, in the centre of the bed, you could place obelisks, with both annual and perennial sweet peas growing up them.
This would fill in the spaces between the trellises without making a solid wall of high fencing right up against the boundary. Plus, the annual sweet peas are very fast growing and if planted early, watered and fed, they'll give you great screening summer 2027. The annuals will give the perennial sweet peas time to get established while also giving you privacy sooner rather than later,
You could do the same on the trellises - grow annual climbers from seed (such as ipomoea or thunbergia) up the trellises while the honeysuckle or roses get established. Again you'll get fast short term cover with an established screen forming in the subsequent years.
This option should give you pretty much decent coverage by next summer if you (a) build and plant it this autumn / winter, (b) buy the perennial sweet peas as established plants (c) sow the annuals indoors early in the season.
On the subject of light - yes plants will block light and will block more light than bare trellis. However plants are more interesting and pleasant than bare trellis. You can be considerate and thoughtful about how you place both the plants or the trellis to get the privacy you want without building Alcatraz for your overly friendly neighbour. !
This is why I've suggested intermittent trellises or obelisks placed away from the fence line. By spacing them with thought, you should be able to create privacy without completely blocking the light. By placing them away from the fence, you're not creating a solid screen which could feel overwhelming for your neighbour.
And all the plants I've suggested will either die back or shed their leaves in winter - so they'll give screening in summer when you're out in the garden, but will allow winter light into the neighbours windows. And in the summer, your neighbour can sit in the sun in her garden if that's what she wants.
Would I prefer plants or trellis? I'd rather look at plants than my neighbours in their garden so I might not be the best person to ask!
But remember - if she can see you in your garden, then when you're in your garden, you can also see her in her bedroom. So your considerate screening will ensure she has privacy in her bedroom too - after all, does Doris want you and your guests peering into her bedroom while you're having a BBQ?