How much it cost and time frame needed for developing platforms like coinbase e.t.c.
It's not about how much it costs, you need to look at several factors... security is the main thing when it comes to wallet platform.
1) You'll need knowledge about how crypto works (creating raw transactions, signing transactions, broadcasting them, etc)
2) Fee calculations.
3) Trusted developers, they can hurt you down the line.
4) Security, you need to know a thing or two about cross-site scripting, SQL injection attacks, and password hashing algorithms.
5) The language you wish to use for your web wallet, i.e: PHP, JAVA, NODEJS, and so on...
6) You'll need to know where and how you'll store funds. Bitcoin nodes can be costly.
7) Do you want your users to have API? Callbacks, Webhooks? If so, you'll need to plan on how to execute that as well.
The timeframe you're looking at would take around 2-6 months.
I hope this helps.