While any Altcoin is swayed by the overall market, finding an Altcoin with a large market cap and large trading volume should be a good estimator of stability. For the cheap mid-price Altcoins, something like Ripple is pretty stable. For the even cheaper coins, you can never go wrong with Dogecoin.
I really think Dogecoin and Ripple are very stable and cheap for now,
Stellar and Waves are also very stable too , the price movement is very good...