Can you please tell me why you want particularly a Steyr LP10? I am asking this question because I had a LP10 and abandoned it after 2 years. I went for a Hammerli AP40 which I always cherished (I love it's looks) and I am still using it with pleasure since 3 years. In my club we are 5 persons to have abandoned the LP10 for other guns mostly Morinis. I started shooting with a pump action AP called FAS and then graduated to the Steyr LP2 (club weapon). Started scoring well with the LP2, thought myself to be a champ and bought the LP10 and never reached the scores of the LP2.
You need to have a very good level of skill to control the LP10 trigger (Champions' gun

The Morinis have excellent trigger mechanisms, much easier to control and hence give a lot of confidence.
Here is a non exhaustive list of the APs used by the regular competitors of our club here in Paris.
8 Steyr LP2s, 6 Morinis (4 electronic & 2 mechanic), 5 Steyr LP10s, 2 Hammerli AP40s, 1 Pardini K12, 1 Pardini K10, 1 Walther LP300XT, 1 Sam K11.
12 of them participated in the Nationals 2012 (4 Morinis, 3 LP2s, 2 LP10s, 2 Pardinis & 1 Walther)
We have a 23 year old very good shooter who is ranked in the first 15 of France in AP and 6th in Free Pistol. He shoots with Morini mechanical trigger AP after having abandoned his LP10

The Izzy is the best option of the two you have selected. Otherwise go for a Morini mechanical trigger 2nd hand or a Pardini K2 2nd hand if possible. Buy an AP which has a perciptible muzzle reaction (natural vertical flip); you will learn pistol shooting more easily.
best regards
tirpassion