In a new position, the first thing that you need to do in the first 3 months to make a good imporessionimpression is to deliver the work. Meet deadlines and do as good a job with the task as possible. The better you do at delivering, the more respect you will have and the easier it will be later to propose and make changes.
The one thing you don't want to do is start out telling them that their software is horrible and their techniques need to change. Even if this is true. You have no chance of making a change to comanycompany policy, software design or tools, etc until you have earned respctrespect through the qualitiyquality and timeliness of your work. If you come in as a person who thinks everything should change to how you want to do things, people will resent you and you will never gain respect.
It sounds like you have started well and it is time to ask your manager for some hands on tasks. Once you do the first task, ask for a code review even if this company doesn't normally do them. It is critical that you get started in the right direction and a code review shoudlshould catch anything that you should know about that no one has told you yet. Don't feel bad about asking for your manager's time, everyone will be less busy once you are up-to-speed.