A few technical indicators may be of some slight value in intraday trading (i don't know anything about the time frame you are wanting to trade in) and it is worthwhile to become familiar with a few, such as the stoichastic and MACD, but a little knowledge can be a dangerous thing.
If you are a new trader, i would strongly recommend that you concentrate on learning how to intrepret and use the market internals, such as market breadth, and the advance/ decline, and possibly the so-called traders index or TRIN. Learn about support and resistance and Fibonacci levels and how to find points on charts called pivot points which are really just points that have some higher than ordinary probability of a price reversal.
You also must become familiar with options and the VIX index even if you are not going to trade options, because options trading does affect equity price action especially near option expirations. Also you will find that depending on what you are trading there will likely be sectors of the market that act as bell-weathers for your instrument of choice, so naturally you will want to monitor a real-time chart of those bellweather sectors. For example many people who trade NASDAQ stocks like to monitor the Philadelphia semi-conductor index, etc.
Personally i would not spend much time studying esoteric and little used technical indicators. One thing you should do is find out what most other traders are looking at and look at the same things. In trading, it does not pay to be an innovator.
And one other thing, while i am in preaching mode, i would not bother with Level II information. It is largely worthless nowadays in spite of all the hoopla you will hear about it. But if you can access time and sales, that is indeed useful.
So, i guess what i am saying is that there in nothing wrong with learning how to correctly intrepret a few of the mainstream technical indicators, but don't be fooled into believing that they constitute some kind of Holy Grail. They don't. In my opinion it would be better to spend time trying to learn something about market psychology and why price does what it does at times (eg., bull and bear traps) than it would be to spend time learning about "odd ball" technical indicators. Oh, and one more bit of advice, don't try to glean anything from real-time data on a time scale anything shorter than 3-min per point, it's "pointless" to do so, unless you are a computer.