It depends upon what you intend to trade to some extent. You will find that many brokers will have their own trading platforms, available as desktop, web and mobile apps.
If you want trading software which is more generic and which includes some programming capability some popular choices are:
http://www.metatrader5.com/en
https://www.amibroker.com/
If you choose a generic product then ensure that it has an API (application programming interface) that works with your chosen broker. This allows the software to take data feeds from the broker to incorporate into charts etc, and to send orders to the broker.
For example amibroker has an API with broker Interactive Brokers:
https://www.amibroker.com/guide/h_ib.html
https://www.interactivebrokers.co.uk/en/index.php?f=5041
Also ensure that you are comfortable using the software. Does it facilitate or detract from your ability to obtain and analyse data and send orders. If it requires some programming how comfortable are you with that ? Also do you need the ability to program the software to extend the capability to manipulate data beyond more basic platforms'
So in summary once you have chosen the instrument you want to trade (stocks, futures, forex etc) and the style of trading (scalping, day trading, position trading etc), look at the choice of broker AND trading platform together so that they facilitate what you are trying to achieve.
Many brokers and many generic platforms have demonstration software that you can load and try out, even if it is with archived data. I recommend that you try them out first to see if you can create charts and orders as you expect. Also download any user guides, API guides etc from the broker or software platform site to see how good the documentation is. Finally look for any user community links on the sites to see the types of questions or complaints that the existing user communities are having , and how they are dealt with by the broker/software supplier.