Hi Sachin,
As you have finance experience, you may give an attempt at SAP FICO module which is of high demand.SAP FICO module refers to FInance & COntrolling. It is one of core modules of SAP. It is tightly integrated with Sales & Distribution (SD) & Material Management (MM) module
Talking of Oracle or SAP, to have good understanding of SAP, how it works, how data moves, accessed....etc you would need basics of Oracle at first. Gradually you may go into depth of Oracles.
If you want to move your career in SAP, there are lot of free & paid stuffs available in internet to boost your knowledge like SCN community, SAUG, SAP TechEd online,SAP Learning hub, Open SAP, Youtube, twitter, Slideshare....etc.
Basic books TADM10, TADM12, TADM 51 will of great help. May also check SAP Basis Administrator Handbook NW Edition by Ranjit Merredy for beginners awesome book.
In case you only wish to work as Oracle DBA (Oracle Database Administrator), you may have a training and certification which can be done with little effort in 2-3 months. This doesn't need any SAP related stuffs and you will be absorbed in industries as Oracle DBA.
Hope this helps.
Thanks
Sriram