You have to get used to pricing things in BTC. I would only trade 2-3 alts for a while to get the hang of it.
However, for the most part, a lot of the trading on Bittrex is done through good price entry accumulation and catching a big wave up. I think day trading would be somewhat difficult on Trex, but I know some people do it.
I just do buy orders at what I think is a good entry. From there, either scale up sells or accumulate for the moon. Gotta learn the BTC price. For instance, I trade a lot of NEM(XEM) and I know the BTC price range that I really don't care what the USD value is. But I've had days where my portfolio is down BTC but up USD.
I guess that's part of my question, is it cool just to totally disregard USD price and only look at it in terms of BTC price?
Also, once I'm in a position, should I care at all about what BTC price is doing in relation to USD?
In many cases, yes, you can ignore USD. You will want to follow for a while to get used to looking at the charts this way.
So altcoins lag behind when Bitcoin's value increases, therefore the BTC price of an alt will go down. However, when Bitcoins price goes down, the alts go down with it. So you cant be emotionally attached to your altcoins. You want to have stop loses to sell when bitcoin causes them to bleed. Once Bitcoins consolidates, the alts will start to correct in price accordingly. It's kind of the wild west in cryptoland. :)