Hi Carol,
I went to Peru with Travelsphere in August this year and had a wonderful time. I wrote a review which you will be able to find in the review section, although you will probably find others relating to previous departures in there as well. Travelsphere's tour is more comprehensive than JY's, so I would suggest that you compare the two itineraries and decide which one you would prefer.
Altitude sickness affects different people in different ways; anything from headaches to difficulty in breathing or walking around so, as Dave suggests, take things slowly and easily when you reach the higher altitudes. The Travelsphere tour is designed so that you ascend gradually (I'm sure JY's would be designed along similar lines) and consequently have the opportunity to acclimatize. Coca tea is supposed to help but, not liking tea, I only tried it once and hated it so I can't vouch for it's effectiveness. It is however widely available and many people on the tour did drink it. One thing I can recommend is that you don't drink alcohol at the higher altitudes - I drank nothing but water with my meals for four days and I'm sure that helped me cope reasonably well, although I did feel completely drained for half a day at Lake Titicaca (12,500ft).
In terms of weather, Lima is affected by a grey coastal fog called 'Garua' from May to September so in August the weather there may not be so good, but once you leave the coastal plain, you should get many clear days as their winter is the high (dry) season in Peru. Personally, I think it's worth sacrificing a couple of days of 'iffy' weather in Lima to get the best chance of seeing the majority of the country in better conditions. We had grey clouds in Lima but wonderful weather in Arequipa (which as Dave says is a beautiful city), Lake Titicaca and Machu Picchu and less than half a day's rain in Cuzco.
In terms of clothing, you would need to take layers for the higher altitudes where it can be very cold under an azure blue sky. Temperatures in Lima are fairly mild and, if you book the amazon add-on, long-sleeves, long trousers and good walking boots are the order of the day.
Peru is one of the most spectacular countries it has ever been my privilege to visit. Landscapes range from high mountains, snow-capped volcanoes and ancient civilizations to hot, steamy jungle, so I would encourage you to book it.
If you have any further questions please ask and I'll do my best to answer them.
Cheers
Mike