The only problem you'll always want one once you've driven it......
Oh YES!
Ok, some of the critics above ^^^^ may have a point, but if they want the Eurobox standards of the coilers, then a Series landy is never going to be for them. No sweat, these machines were designed in the '40's with on-going mods through to the '70's, so there is absolutely no point in comparing them to Eurotrash.
So, you now have a reasonable idea of the pitfalls from the above posts, but they can all be mitigated in way or another. Your major issue is deceiding whether to do a sympathetic period restoration, or to rebuild a landy incorporating as many features to mitigate the downsides.
For me, total brake system replacement is a must. after all, you have no idea of who has been mucking with it and what they have done, so replace Shoes, drums, snail cams, springs and cylenders. All parts are still readily available to original pattern, and the brake system will work well. If you want to stop on the spot, put in a servo ex seriesIII.
Then put on some sensible boots, with plenty of tread. - if you ain't got any grip it won't matter how good your brakes are.
Steering: - I use the 15" wheel from Paddocks - it reduces a lot of the vagueness....then you can work through the rest of the steering system, oiling, greasing and tightening as you go.....it does work, and likely that it is donkeys since it was last done (if ever)
suspension: Parabolic springs with Procomp 3000 dampers and your roadholding/cornering improves immeasurably.
Heating - often well worth draining, & flushing the cooling system several times, then checking the gills etc on the heater.....if it's the round one, often the fan motor is 'tired' so total replacement is the best result, and if it will fit, put in the flat panel heater from the later IIa - better (2 speed) fan, better heat exchange.
Leaks....replace rubber seals as necessary around doors & windows and if it's bodywork that is the issue, then tighten/replace bolts as necessary...some also seal with a bit of silicon.
Lights - if you have a alternator driven -ve earth system upgrade to halogen, if you don't...then consider for later.
and so I could go on.......
......best place for series IIa advice is from the series 2 club....
Welcome to the Series 2 Club There are some seriously knowledgeable folk there.
But, when you have finished your restoration, and after all that effort.....when you have passed the MOT and are driving back from the testing station, try, just TRY not to have the biggest grin on your face !!!
And as for speed and economy - I have a 1958 series II (with a III 5 bearing engine & servo assistance) it regularly turns in 65+ on the flat (sat nav rated) and at that speed, 20+ mpg. My standard IIa will hit 70 and averages 22mpg.
Have fun!