I used to drive a hyundai coupe before my and trust me, that was 10 times worse than the to bang into reverse. One solution ive found is, that if you go forwards a slight ammount (maybe a centimetre) it goes into reverse ALOT easier. I only have reversing problems when its been sat out over night, or i havent driven it in a couple of hours (maybe it sticks or something).

Also, as for wheelspinning - Take it very easy on the throttle, unless you want to spend alot on new tyres. Learn to control the clutch better, dont bring it up as much, or use less gas. Sometimes, when its icy/wet, all i do to start moving is slowly lift the clutch up and the car will start moving without the use of the throttle. Then just give it a little gas and bang it into 2nd. I always drive in 5th gear also..even on 30 roads. Hope this helps.