Engine swap and Automatic conversion 1965 Valiant

You need to match the engine and transmission. A "correct" engine would be 1963-1967. The matching and "correct" transmission would be 1963-1965. Around 1968 (experts can correct), the crankshaft's pilot hole was made larger, as was the matching snout on the transmission's torque converter. You can buy a ~$25 adapter ring to fit a later engine. In 1966, the transmission and driveshaft changed to a "sliding yoke". Check Google Images to insure a 1963 pushbutton panel will fit your 1965 dash. My 1964 has dash pushbuttons, whereas my 1965 has a floor shifter. I recall that no 1965's had dash pushbuttons and the whole dash layout changed. But, they used the same cable-shift transmission. If you install a floor-shifter, you also need the small weld-on bracket to secure it.

As mentioned, the driveshaft may need to be shorter for an automatic, but many shops can shorten one and balance inexpensively. The front "ball and trunnion" (aka "Detroit") "sliding U-joint" is strong and reliable, but parts are getting rare. I have enough to keep my 64 & 65 A's running for life. I posted all PN's several times, and you occasionally get lucky on ebay (I did). You can also have a custom sliding yoke fab'ed. Jeep Cherokee owners used the same PN and deal and pioneered that. I have seen one for them on ebay ~$150 for any custom length. You could use a 1966-1967 transmission to get a sliding yoke output. Can even use a later one if you get a custom torque converter or a later one and change the input shaft to later style.

There are many other options, if you don't care about "correct". A Magnum 5.2 or 5.9L V-8 will bolt-up to a later 904 (or 999) transmission. That gives cheap MPFI and roller lifters. You can even use the better Magnum transmission (overdrive), but need to rework the transmission tunnel. A V-8 also requires a different steering cross-link, and denting in the oil pan unless you get a 1964-66 oil pan.