I want to buy $100k worth of Bitcoin and move them to an exchange.
I believe you might be confused. You need to buy Bitcoin from an exchange. So you're starting at a exchange, therefore you won't need to move your Bitcoin to another exchange. What you should do is move your Bitcoin to another wallet, that isn't on an exchange. It's safer to keep your Bitcoin off an exchange.
1. Are there better alternatives to Coinbase in terms of purchase fees and transaction?
Sure! Let's start with where you live, what Country? Coinbase doesn't operate in every Country in the world (ore even every state in the US).
2. Wouldnt it maybe be cheaper to buy LTC, move it to the exchange and buy BTC with it?
No. Making two transactions over two different blockchains will incur two different sets of miners fees. Keep the transaction as simple as possible.