I am really thinking about investing over $1000 of my savings into Bitcoin. Would this be wise? Is BTC safe and stable at this point?
Nope. Just give it a year or two though and then perhaps it will be stable.
This software is in BETA stage for a reason. There are still unresolved matters with successful-and-easy attack scenarios.
Those need to be resolved before BTC can become serious currency.
There is also a question what will happen if quantum computers come into play in 5,10 or 15 years. It will either kill BTC totally (low probability) or render it useless and freeze all transactions until it is secured with quantum-computer encryption algorithms (more probably).