I'd say at least 6-8 feet clearance.
On subject on cycle lanes .. I use them if them make sense to me. Have to say some of the cylcle lanes around here are just daft. I do thank Steve C of the JJs here - for giving me a contact name to complain to as Ambleside in particular is a disgrace and an affront to commone sense! On this - I believe he is pro-safety
I confess that to some extent I am a lucky man - live in the Lake District - which means good scenic drives, horseriding, fell walking and pedal cycling.
As I live in one of the UK's major holiday resorts and ride and drive for pleasure (no matter how many times I see the scenery here - am gobsmacked by it all - and by birth am a Dalesman - so rural life is in my blood really). Anyway - one of the benefits to me is that I have some of the best places to ride horse or bike or drive my car in this area - and an addend bonus is tha t we meet people form all over the world here.
So - based on what a 19 strong party from Sydney, Australia declared to me on one of my fave rides around Ullswater and and an American party at Buttermere.... am going to say

to all UK drivers
cyclists for cycling club in Sydney, Australia, and cylcling club from New Jersey, USA on holiday here and really nice chaps tp whom I mentioned this site wrote:
Drivers in Britain - and we have been touring the Yorkshire Dales, York, Durham, Lancashire, Scotland Wales, Derbyshire, Shropshire, Cheshire, Liverpool, Manchester. ... all seem very courteous and give us space, time, courtesy and consideration
I think this is indeed worth mentioning as it seems to indicate that we are indeed a nation of safe drivers on aggregate
As regards wearing a helmet - wear one as matter of course.
As regards a high viz bib or tunic - lots of really stylish wear on the market these days and I do have a selection of suitable attire. I also have various light weight lycra garments - shorts , three quarter and fulkl length and in a variety of colours too.
This is a rural area and we do not always have street lighting. It's as my sister-in-law once pointed out on C plus (they moaned but they know deep down she's right

) - you really do need this gear if only to be spotted in the dipped or high beam head lamps in these areas. Anything which makes you stand out and visible is a bonus.
Lights? Like IG, Kriss and Mike. an rest of family world wide .... Wildy and self use Lupines. You carry a spare battery in your kit - but normally I'd expect about three hours at high power.
If on budget - agree with IG over the Knight Light Adventurer. Vistalight is £100 and battery will power for just 45 mins on full power.
Cateye ABS (about £150 - 3 hour battery) or Lumicycle (£160 and 4 hour burn time battery wise) or reasonable buys.
My advice anyway....