In my opinion. A bicycle deck is the best deck to use. Just because every one knows about it and it doesn't rise suspicion. Using a deck someone has never seen before would make them already think your going to cheat. In the end, a little less magical.
That's actually a common misconception. A deck like any of the Split Spades/White Lions aren't very exceptional from the perspective of the spectator, especially when you consider they have single-color backs and Bicycle faces (custom Ace of Spades, Joker and select faces on the court cards, but the overall design is fairly traditional). Give them something they can identify with and you'll be fine. Bust out a pack of Bicycle Karnival Dose Redux and unless your audience is composed largely of Goths/emos, you might raise an eyebrow or two - but even then, that's all.
The things I think will throw a spectator off the most would be:
- cheap-looking off-brand generic faces, because the cheapest magic decks are made thusly,
- bizarrely intricate back, like the old DeLand marked decks
- cheap manufacture, stock, etc., (see first reason)
Blaine's entire series of decks have standard USPC faces with the exceptions listed above, which many spectators wouldn't notice or care about. If you want to and can for this trick, hand the deck over to the spectator to examine. What I do is I spread the cards out, ostensibly for the purpose of checking that there's "nothing missing, damaged, misprinted, etc.", while the reality is that I'm letting the spectator see the cards aren't gimmicky in any way - without actually drawing attention to it. It helps that I often use a fresh pack when performing for the patients at the hospital; they see I'm opening a sealed box and the cards are all in original order.
You tell a spectator that it's an "ordinary deck," warning lights go off in his or her head and they'll distrust the deck. Let them see it for themselves, and they're convinced it's legit.
EDIT: Most people would accept a Bicycle deck as OK, if it was a brand they knew well. But fellow magicians know better! If you have one in your audience, or just someone who knows enough about magic, a Bicycle deck would do the opposite - set off warnings that the deck might be gaffed in some way. More gaffs come in the Bicycle Rider Back than any other design, hands down.