In general Uzbekistan has a hot, dry, desert climate, though there are differences depending on the particular regions you're visiting. Generally though, in June and July you can expect temperatures well into the 40s (degrees Celsius) during the day, and dropping to 30 or so at night. It's very unlikely to rain during this period. On either side of that, around April-May and September-October, it’s quite comfortable with temperatures around the early 30s during the day (though it's possible to experience late 30s or early 40s during these times as well), and dropping to the mid teens overnight. It's still unlikely to rain. Winter temperatures usually don't get above 10°C and regularly drop to below 0°C, and there will be a fairly constant layer of snow on the ground in most places.
Based on weather, depending on when you’re visiting Uzbekistan, you could need anything from shorts, t-shirts and swimming clothes, to jackets, boots, hats, scarves and gloves.
You might be thinking of Uzbekistan as an Islamic country and therefor be wondering about what’s appropriate for you to wear, but you really don’t need to worry about this aspect. They are technically Islamic, and although you will come across some practising muslims, for the most-part Central Asians have a very complicated and unusual relationship with religion. So what you’re picturing as “Islamic” in relation to places in the Middle East for example, is not what you’ll come across here. Having said that, they do tend to be more conservative in many ways than most western people, though for the vast majority it’s not in a religious way. You won’t see many local women showing much skin, especially the older generations, though plenty of the local Russians will be, and it’s certainly not unacceptable for you to do so. Likewise local men don’t often wear shorts, but it’s not because it’s inappropriate, it’s just not fashionable. There are one or two very specific places where females may be asked to wear a scarf around their head.
So in general, just wear whatever is appropriate for the season, but if you’re female, have a scarf in your suitcase just in case.
There will be a fair amount of walking throughout the tour, but mostly on flat, paved surfaces, so as long as you’re comfortable you don’t need to worry about anything specific. There are a few times when you might be walking over dusty, sandy or rocky ground, depending on exactly where you’re going, but nothing that can’t be done in your normal trainers, flip flops or sandals.
You’ll be transported between your accommodations by buses or cars, depending on group size, with plenty of space for luggage, so you can really bring whatever kind of bags you like. You won’t need to carry your own luggage very far at a time – just cars to lobby to room and back, and it doesn’t need to be compact to fit into small areas. Hard suitcases, soft suitcases, wheels, no wheels, backpack, whatever you like is fine.
Pharmacies are aplenty in Tashkent and Samarqand, and some basic medications like paracetamol are extremely cheap. Outside of the two main cities there are still pharmacies, but the smaller and more rural you’re going, the less availability there will be, and in much of the country, there isn’t any access to medical supplies. As such, it’s definitely a good idea to make sure you’re stocked up anything like that that you may need and if you have any specific medications that you regularly need you should try and bring them with you if possible.