Yep.. I have a few myself! UCA is definitely a 3/4" U-matic tape.
Look on Ebay.
The best machine out there is the Sony BVU-950 -- it is a broadcast deck with a built in TBC -- however, if you know nothing about video machines, you might want to get just a player deck.
Example of a cheap player:
I wouldn't pay more than $ 300 for the top of the line deck. Just keep watching them on ebay. Sometimes they are dirt cheap.
Look for Sony VO-, VP- and BVU- series decks. If the tapes are very, very old you may actually need a top load Type 2 Deck like a VO-2860 to play them. The later Type 9 decks do not handle those tapes very well. The BVU series machines are broadcast decks. They have better head switching (in the vertical interval). Many TV stations used the pro machines instead of the broadcast series because of the price difference.
Another thing: you will probably need to repair some of the tapes if they are from 1977 or older. I suspect that upon rewinding the tapes, the take up reel will come loose from the supply reel inside the cassette. In that case, you need to take the screws out of the back of the cassette and rethread the leader onto the take up reel. Sometimes you will need to get a new cassette and put the old reels in the new cassette for them to play correctly.