Coinbase offers LTC and ETH that you can trade USD for. They’ve mentioned several times now they’ll offer BCH at the beginning of the year. Try not to think of it as buying so much, it’s trading. Altcoins is everything that isn’t Bitcoin, right? You want to buy (trade for) Altcoins, that means you’ll need to sell (trade your) Bitcoin. I’m familiar with Coinbase.com, Cex.io and Kraken.com to trade my USD for BTC. From there I like Bittrex.com and Kraken.com to trade my BTC for ALT’s.
Hopefully this helps you out, try to be careful. Research is key. There’s a lot of really informative people out there hosting their own YouTube channels, sharing their information about crypto’s. A couple that continue to help me out are:
Boxminingdaily and Dollar Vigilante.