Hi and welcome!
Here's the log and the kingdom presented in a way that's actually not unbearably painful to try to decipher:
gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20160717/log.0.1468796089135.txt (http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20160717/log.0.1468796089135.txt)
(http://wiki.dominionstrategy.com/images/c/cf/Talisman.jpg) (http://wiki.dominionstrategy.com/index.php/Talisman) (http://wiki.dominionstrategy.com/images/e/e0/Taxman.jpg) (http://wiki.dominionstrategy.com/index.php/Taxman) (http://wiki.dominionstrategy.com/images/5/51/Band_of_Misfits.jpg) (http://wiki.dominionstrategy.com/index.php/Band of Misfits) (http://wiki.dominionstrategy.com/images/6/66/Cache.jpg) (http://wiki.dominionstrategy.com/index.php/Cache) (http://wiki.dominionstrategy.com/images/0/0a/Ghost_Ship.jpg) (http://wiki.dominionstrategy.com/index.php/Ghost Ship) (http://wiki.dominionstrategy.com/images/9/9d/Harem.jpg) (http://wiki.dominionstrategy.com/index.php/Harem)
(http://wiki.dominionstrategy.com/images/8/89/Raid.jpg) (http://wiki.dominionstrategy.com/index.php/Raid) (http://wiki.dominionstrategy.com/images/d/df/Hamlet.jpg) (http://wiki.dominionstrategy.com/index.php/Hamlet) (http://wiki.dominionstrategy.com/images/0/0f/Pawn.jpg) (http://wiki.dominionstrategy.com/index.php/Pawn) (http://wiki.dominionstrategy.com/images/5/51/Farming_Village.jpg) (http://wiki.dominionstrategy.com/index.php/Farming Village) (http://wiki.dominionstrategy.com/images/3/36/Smithy.jpg) (http://wiki.dominionstrategy.com/index.php/Smithy)
Raid, Hamlet, Pawn, Farming Village, Smithy, Talisman, Taxman, Band of Misfits, Cache, Ghost Ship, Harem
On that board, I would definitely build an engine. I'd buy a Talisman (only one copy) and get a ton of Smithies and Farming Villages, and at least one Ghost Ship on your first $5 turn. Taxman is probably good here, because that's a way to potentially get lots of payload without adding too many stop cards into your deck, which is important because there's no trashing so your payload should preferably take up as little space in your deck as possible. For that same reason, I would avoid buying any Treasures other than the first Talisman and maybe one Silver in the early game (you can buy Platinums later on when your engine is already working).
If you look at your opponent's deck, you can see that his mistake was that he had tons and tons of cards in his deck and not a lot of drawing power — he could only draw up to 16 of his over 30 stop cards by the end of the game, and for the longest time, he had hardly any draw at all. An engine that played a Ghost Ship every turn would be easily able to crush a big money strategy here, since it's so hard to do anything with just 3 cards in your hand as a big money player in a Colony game.
EDIT: Here's a pretty bad example of how it could play out, because I don't have all the expansions so I had to substitute a couple of cards for significantly weaker alternatives (this is one of the rare boards where Farming Village's ability is actually not entirely useless, and Squire is a lot worse than Hamlet) and the bot played horribly, but at least it's something: http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20160718/log.0.1468842118724.txt