It is very important that you follow all the necessary University application steps in as set out in the University's How to apply- International Student information.
You should follow the process as closely as possible and you can make an application go quicker by ensuring that you are providing all information and documentation promptly when required. It also helps Admissions staff if you are able to submit everything needed all together. It causes delays when staff have to ask you for key information or search through various submissions and emails in order to try and work out if they have everything they need from you in order to make a decision.
It also causes delays if you submit lots of documentation that the Admissions staff do not need to see. This is because it will take them time opening everything up and trying to work out what documents are what and what they actually need. You can save them time by just uploading what is necessary and clearly labelling the attachments.
If you have studied in the UK before you should expect to provide evidence of all the UK visas you have had for previous study. Providing these from the beginning will help staff assess whether they are able to issue you with a CAS. If you have lost visas/copies and they are unable to work out exactly what the start and end dates on the visas were, they may ask your permission for them to check these dates with the Home Office. This is a common and standard process and so should not worry you.
Once you have your unconditional offer you can start preparing for your visa application. You can partially complete the Tier 4 form and gather your documents, even if you have not yet received your CAS. You would then complete the visa application once you have your CAS (which will be emailed to you).
Comprehensive information around applying for Tier 4 and other visa categories can be found on the ICL Visas and Immigration pages.