This is my first order from ippodo but I know that their teas are good so you're in safe hands.
Not sure I can recommend much as I don't know your tastes -- I would suggest having a good read of what's on ippodo and
Types of Japanese Green Tea to get a better idea.
Sushi bars, at least Japanese ones, normally serve (sencha) konacha, which is the broken up leaf left over from processing the actual sencha. Ippodo sell gyokuro, sencha and bancha versions.
As for matcha, unless/until you're prepared to buy at the very least, a bamboo whisk, I'd stick to loose leaf teas as it really does need the right tools.
That said, I really enjoy matcha. It's more...intense, perhaps, than other teas; stronger and more bitter (though I don't notice that so much, myself) but a good matcha shouldn't be overpowering or undrinkably bitter. Some will be lighter, some creamier in flavour. I would pick a mid-range matcha from ippodo; perhaps one of the 'high quality' tins.
Matcha's not cheap -- I'm drinking the sayaka no mukashi at the moment but I don't think you need to spend all that on your first try. I would suggest either the kan no shiro or ikuyo no mukashi, perhaps...