All of the above are causes. A worn front u-joint will also create problems. Popping out of 3rd gear is a common problem with these transmissions. There is a fix which places a spacer between the front bearing and the gear. You must also remove the spacer on the first row of needle bearings for this to work. This moves the gear further into the syncronizer. pre68Dave has info on this on his site also.
Popping out of 2nd and 3rd indicates to me that all of the above could be in play. In any event a replacement syncro drum and the 2-3 shift fork are in order.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine