First of all you need to follow STLC if you want to test any software/Website properly with software testing standards.STLC is same for all. It does not matter what you are testing so STLC is base to start and complete testing with quality.
Manual Testing - In most of application there are some areas which really need manual testing. So you need to find out that how much manual testing your web app. need.
Automation Testing - It is very useful to create automate test scripts which help to reduce testing time , resource and provide reliable result if you write correct script.So when you say how can you minimize process then I like to say that automation testing is good for repeated things in app. It also helps in regression testing.
So , Before start testing if you define that how much manual testing we will need , for which functionality we will do automated script then it will help you to get time estimation for that app. testing. Also make sure that you can estimate approx. time for any app. testing only if requirement are fixed. Now a days , it is common that requirements are changing very frequently which is not good to product top quality result.
Which testing you need to do for your web application it is really depends on application concept. Some web app. require only functional & non-functional testing , some require security testing also , some require other testings and a lot more.
In your case for "Financial Web application" , you should do testings like functional , non-functional , security , smoke , usability etc. If you think that there will be lot of traffic on your site when you do LIVE it , then you can also do Load Testing to measure your app. capacity.
You should create Test cases , Test scenarios and Bug report which makes testing more standard. Also it is require to update test cases regularly when requirement changes otherwise it never help to find new bugs.
Useful automation tools :
1 - Selenium with web driver [For functionality testing]
2 - Jmeter [For Load testing]
Also make sure that before start any testing , you must have full understanding of web app. which you are going to test. So requirement understanding is very important.
Hope this help you to minimize and set proper testing process.