Embankment and Charing Cross are also perfectly fine stations for access to Covent Garden, depending on where you're coming from. Plenty of buses down that way, too (there's also the RV1 tourist bus that links Borough Market and Covent Garden, not to mention a number of ferries).

Do ditch the suitcase. You won't be able to drag it round the crowds at Borough or the cobbes at Covent Garden. Airport and mainline stations will all store it for a fee, or you can try to blag it at a large hotel

But the real question is - what do you want to do? There are loads of interesting markets and shopping districts around the city, but perhaps less 'classic' London, and less tourist-friendly. This may be a positive or negative to you.