I find myself in a similar situation. I'm quite anxious to get involved with the whole concept of cryptocurrencies, mainly BTC+LTC.

Ultimately, I'd want to mine BTC but I kind of feel I missed that train. This is a poor attitude. Instead of grieve about missed opportunities, I try to focus forward. While LTC is not BTC, it may be a fun and educating introduction to the whole concept. So I might go for LTC at first and then involve in BTC (mining) as my investment strength arise. As you also realize, to have a nutritious BTC mining today one need to spend quite some fiat got get there.

TL;DR: Begin with LTC. Gain knowledge. Advance to BTC. Gain profit.