"Wide-spectrum" or "broad-spectrum" sunblock is sunblock that will block both UV-A and UV-B radiation. UV-A is what causes skin cancer, while UV-B is the culprit in sunburn. Pretty much all sunblocks will protect from UV-B, but blocking UV-A is trickier, and blocking UV-A is what helps to keep you feeling cool.
Generally, you want to look for a sunblock that contains Parsol (Avobenzone) &/or octyl methoxycinnamate, and also Titanium dioxide. These come in all forms, but as I said, I like the fine spray best because I find that no one complains about using it regularly, as my family will with sunblocks that have to be rubbed in. My band of palefaces gets sprayed every 60-90 minutes; we reapply while in ride lines (being careful not to spray bystanders, of course.)
The most commonly available spray that I like is the Coppertone Sport spray in the royal blue bottle; this tends to be the brand available at wholesale clubs and places like
WalMart. I really like the Hawaiian Tropic Ozone Sport Spray, but I can never find that where I live; I stock up while in Florida. Another good spray is Bull Frog Quik Gel Sport Spray, but the bottle is small, and it's very expensive. For faces/ears, we use either Neutrogena wax stick, or the HT Ozone wax stick (a little cheaper); these stay where you put them and out of your eyes. I know a lot of people who swear by Water Babies, but I find that the scent of that one tends to attract bugs (way too perfumey, IMO.)
For babies, you really need to devise a sun canopy to use *in addition to* whatever sunblock your ped. recommends. For the stroller, go to a fabric store and get a yard or two of somewhat loose-woven white cotton, which you can drape over the hood to form a tent. (Note that sun WILL actually penetrate this, even though it feels shady.) Occasionally take your spray bottle and dampen the fabric; that will cool the breeze coming through it. Also, lining the stroller with a white towel will keep baby cooler in a dark-coloured stroller. If you are using a sling or snugli, carry an umbrella over the both of you; a golf umbrella with a reflective surface is the most effective. If your ped. advises against applying sunscreen at all, I'd go for a poncho &/or stroller tent made of solar protective fabric; you can get it on the web, here's one place:
http://www.solarveil.com/fabric.asp
As for mosquitoes, we use Bug Off wristbands. They are made w/ citronella and geraniol, and work pretty well. In fact, they tend to be so strong that we wear them on our ankles instead of our wrists; you can get a headache from the smell if it's too close to your face. For babies, we put it on a leg of the stroller, near a wheel.
SPECIAL TIP ABOUT HEAT AND LITTLE KIDS: Little kids are the most at risk for dehydration, because they tend to get too excited to remember to drink, and they don't tend to tell you if they are feeling odd. If your kids are small enough to be accompanied to the toilet (or in diapers) make it a point to note the color of their urine. It should be a very pale colour if they are properly hydrated; if you can clearly see yellow, they are not drinking enough! Also, with really tiny babies, the soft spot will start to sort of 'sink in' if they become dehydrated; give them fluids immediately if you see this happening.
Her first trip was at 5 months and she is now 5years. It was already mentioned but the clip on fans from one Step Ahead are amazing. We used to get 2 and position them on the stroller one on each side of her. Make sure the hood of the stroller covers everything. You may want an extra attachable strooler umbrella as well for those hard to reach angles that will result in sunburns. Sunscreen everywhere! Especially behid the ears on kids with short hair or pony tails. Also on top of head at hair part. My DD would only keep her hat on so long then she would do her best to drop it out of the stroller. We finally got her the type that velcro'ed under her chin which lasted a little longer. Old Navy used to have them all the time. Now we still use her stroller for various reasons,( safety, keeping track of her, crowds,and exhaustion) but on really sunny days I will dress her in her special swimsuit. It is by Solartex.com It loks almost like a diving suit but lose and light. pretty colors. one piece that zips and it has built in like 45 spf protection. Still use sunscreen and hat on exposed parts but it works wonderfully. We live in So Fla and my daughter is blond blue eyed and fair and she has not once been sunburned. These suits look like one piece short sets in cool colors and are great for when they get so hot you have to send them into the fountains. They dry quickly and are comfy. Aslo, remember to bring a cup because every walk p and sit down restaurant will give you free ice. all day!! Good luck 
