What's the worst possible response to your first offer? IMHO, its "we accept." Fortunately, I've never heard that response. There is either a counter, or (more commonly with REOs) no response at all.
I use just the inspection and financing contingencies. Those make my offer's weaker, but give me some protection. Personally I dislike contingencies like "contingent on partner approval" which to me sounds like "I'll back out whenever I want". I'm quite sure that's what's meant, and I'm sure the seller recognizes that, too.
If I received an offer with a "if I get another acceptance this one's withdrawn", and I was interested in pursuing that offer, I'd cross that out on my counter.
Another thing to do is to put in a fairly short acceptance period. When I make offers on the weekend, I put the upcoming Friday as the acceptance deadline. That way next weekend's searching starts with nothing on the table. If the seller is interested, they can counter, and I'll certainly listen. But they can't accept my offer after the deadline and obligate me to buy.
I also use the "earnest money to be provided within 48 (or 72) hours of contract acceptance" clause rather than providing earnest money up front.
There's always some chance a deal will fall apart after you do have a mutually executed contract. So, even if I had to acceptances at about the same time (its happened once), I would pursue both until my last opportunity to bail out.