I think I've finally decided on a bike. A Diamondback Podium 3, Shimano 105 stuff etc. Seems to be a great price and is in my price range. The local Sport Chalet store has 56 & 58 sized bikes so I'm going to go over and give them each a test ride. My concern is that I weigh approx. 200-205# and the spoke count on these wheels is 20/24. Since the bike is so inexpensive it would leave me room to upgrade the wheels sometime in the near future, but my question is... will those wheels be durable enough to keep me going through summer at my weight? I have the advantage of riding on pretty smooth roads here in So Cal so I guess that should be factored in too.

I weigh 20 lbs more than you so I can answer this. Yes, they will be fine. Wheels are really about the build honestly. Some will tell you that you MUST have 32 spoke wheels as a clyde or you'll break spokes non stop. At 225 my current wheelset is the Boyd Rouleur with 24/28 spoke count, my wheels are great with not flex at all and they only cost me $400. Ride the stock wheels until you decide what you want to add later.

You'll be fine as long as the wheels are made decent...even my old Shimano R500's held up well (also 20/24) and I am 200.

All other things being equal more spokes would be stronger. But as Seymour said the build is as important as anything. Unfortunately OEM wheels can have a problem there.

Here are a few checks you can do yourself:

Check to see if they are true by spinning and watching for both vertical and horizontal changes between the rim and brake pad.

Check to see if the spoke tension is even by plucking and comparing tone. All the spokes on the front should even. On the rear, the drive side will be tighter, but each side should be even.

The biggest thing that gets neglected on cheap wheels is stress relieving. An obvious sign of this is pinging noises on an initial ride, but if the wheels have been ridden some then tension or trueness issues will be a more likely sign.

Mostly correct, but the pinging is not usually related to the lack of stress relieving but rather spoke twist. Most low spoke count OEM wheels on modern bikes have aero spokes so twist would be apparent just by looking.

the mavic aksiums on my bike are 20/20 and I'm about 225, haven't even had to true them in the 2.5 yrs since I got the bike. statistically speaking, at that price range the wheels are likely going to be tank-like in weight and durability. usually won't be a problem until you get into stock wheels on high end race bikes or aftermarket wheels.

The number of spokes is way less important than the strength of the rim, of the spokes to a lesser degree, and the quality of the wheel build. For an analogy, the number of pixels in a camera doesn't mean much these days, I have a 16 megapixel Sony point and shoot and an 8 megapixel Canon SLR that blows the Sony away in terms of image quality. It has a better lens, larger pixels to gather more light, etc. But it's harder to know all the details, so they market cameras on pixel count, and then they cheap out on other things to achieve a big number. That last part isn't exactly true of wheels, but the point that you need to look at more than just a number is.

Have the wheels retensioned after about 200 miles. Then, ride them until you start having trouble with them, and consider a replacement at that point. Fulcrum Racing 7s are cheap, heavy, and indestructably strong.

Agreed that twist/wind-up will also cause pinging, but in either case it is a sign that the wheels were poorly built and will need attention.

And as you pointed out, wheels with aero spokes already have a visual indicator of wind up, so if these wheels are pinging it is something else.

Thank you everyone for your input.