The calibre is up to you , but after shooting a lot of rabbits over the last 40 years I dont use .22 any more. The smaller calibre is easier to place over 35 yards in my opinion, but then you need to be in pretty good conditions and rested/supported, with a known distance to do that anyway.
Rangefinders are all pretty good , MTC, Bushnell etc all for £100 -£200 and yes the laser is invisible.
I dropped on by buying a mates Leica rangefinder at the right money but they are very pricey new. No you cannot use them for HFT unless you set the courses, but it will get you used to estimating and checking distances by eye, so its good training.
Regarding crosswinds and heavier pellets, the theory is good but I dont think about it too much....Wind is not consistent along the whole flight of the pellet, so even if you know the wind speed and direction you will be guessing the effect on the pellet. In HFT you will sometimes see pellets lifting up when you expect them to go sideways. If you can work wind out perfectly in any calibre you will win the UKAHFT and Worlds combined.
About a month ago, myself and Chris C one of the posters above, were shooting Sillys (metal targets) at Redfearns,and the strong sideways wind was lifting the pellets up
1 mildot at 45 yards, and almost nothing sideways. The hazard tape strips were blowing full on side ways, but the pellets didnt follow suit. Also when you see snow going upwards around a target, you know that you are trouble.
9 out of 10 shots on a HFT course I shoot straight down the line!!
Seriously if you stick to one calibre though, you do get used to knowing how much to allow for wind, but its always at best, an educated guess.