The IDF has used quite a few different type of tanks operationally over time and I wondered which models they preferred to use? Was that choice based on performance or parts availability?

I would think it's their home grown Merkava,unlike the imports,they took all the lessons they learned over the years and designed it exactly to their own specifications.Crew survivability being very important to them,hence the forward mounted engine.

The reason why Israel used so many different types of tanks was availability. So many nations had arms embargoes on Israel that they had to get what they could when they could, even using captured tanks.

Finally with the Merkava, they have a tank they have near total control of (not sure of some of the parts used). The only problem is cost and production, which is why they still employ other types.

I expected the Merkava to be their vehicle of choice. Sometimes we debate the relevance of one vehicle over the other. I was curious which (from their experience) they preferred from all of the foreign made tanks that they have used.

From what I've read the preferred tank, or MBT, from a foreign country was the Centurion. The IDF used the M48's, M60's and Soviet tanks more from a "bird in the hand" availability than a real want.

The preferred tank was the Centurion with the Chieftain trailed but never bought due to a embargo
A great what if missed

As Gary (rightly) pointed out, it was rather a matter of availability than preference. The 50's and the 60's are considered the "french era", as a large portion of the IDF equipment (and almost all of IAF's) was French made.
After the '67 war de Gaulle's government imposed an arms embargo on Israel which forced the IDF to look for alternative sources. From the 70's the US strategical interests shifted : in order to counterbalance the huge amounts of Soviet weaponry flowing into the Arab states, Israel started to receive US aid, mostly in forms of arms.
As for preference, I would say the Centurion was the IDF's first choice as its MBT. Despite their age, they were kept in service till the early 90’s. The Centurion's main advantage over the M48/60 was its suspension: it could cope with the harsh terrain of the Golan Heights way better than the Patton's torsion bar system.

Many of these tanks had and still have an "afterlife" as heavy APC's (Nagmashot, Nagmachon, Nakpadon) and combat engineers vehicles (Puma).

And that it is. In 2004 the 401st "Iron Tracks" Brigade (the last regular brigade equipped with Magachs) finished its transition to Merkava 4 ; since then "Hey'l HaShiryon" (hebrew for armored corps) relies solely on Merkavas 3/4 and their sub variants.

I'm not sure but I suppose that the Patton variants held out longer in service than the Centurions because they were newer and more easily upgraded.
The Magachs served in reserve up until 2014, while the Centurions were released from service in 2005, except for their APC variants.

Now, if I understood correctly, in the 1973 war, Centurions were used in the Golan Heights due to their tracks being full metal and worked better on the rocky basalt. Pattons were used in the Sinai front due to their tracks.

Correct mate, plus they kept coming through US aid, while the Centurions fell under embargo.

Not entirely true. Tracks can be replaced - suspension not. As said, the Centurion's suspension system could take much more punishment than the Patton's delicate torsion bar system. That was the reason that the two regular brigades assigned to the Golan Heights (7th and 188th) kept their Sho't Kals till the Merkavas arrived, while the two southern brigades (401st and 500th) were equipped with Magachs.

During my army time on the Golan Heights in the mid 90's there was a Magach platoon/squadron (Yanks, Britons, pick the right one...) rotating regurarly from one of the southern brigades. As Merkava guys, we always felt sorry for the poor bastards with their obsolete Magachs spending more time under them than in them fixing their suspension, while we were sailing through the moon-like terrain like knife in butter.

A short explanation why the Sho't Kal was preferred over the Magach on the Golan Heights :

http://www.globalsecurity.org/military/world/israel/shot-kal.htm

Some more info on the Sho't Kal :

http://www.tanks-encyclopedia.com/modern/Israel/Shot-MBT.php