The weather when I was there was perfect - not a cloud (we were above most of them!). Check the internet but the best times for the trek tend to be UK spring and Autumn - that's when the summit attempts tend to take place as the weather is best. You should be prepared for wet weather though, and just like UK winters, if the weather is good it can often mean it is colder than if there are clouds about.
Clothing:
My advice is layers! It's really really cold at night and in the morning (up to -25). Get yourself some good thermal underlayers for a start. Then non-cotton t-shirts (available from most trekking shops) as they are warm but dont stay wet (as you will undoubtedly get a sweat on with all that walking!) Next layer should be micro-fleeces. They are really light, easy to dry and full zips at the front make it easiest to adjust temperature. Finally, waterproof clothes are a must (coat, trousers and socks). Even if it isn't raining, they are a really good barrier against any wind or moisture and you will be staying in cabins with no heating. Hats, sunglasses, gloves and a scarf are all a must as well. Really try to avoid taking ski jackets or salopettes as they are too big and heavy and you'll get too hot as you walk in the daytime sunshine!
Footwear:
It's really important to get a pair of walking boots which cover your ankles. Some people will tell you that you could walk to base camp in trainers - which is true. But no.1 trainers aren't waterproof, and no.2 any slip on the way and you really risk hurting your ankles (hence the importance that they are covered!) It is also really important that your footwear is waterproof (for obvious reasons). My final piece of advise is to go to boots and get 'Compeed' blister plasters. If your shoes give you blisters (like mine did!) put the Compeed on the night before you walk - it will last for days and should stop you getting blisters in the first place! I wouldnt have made it without Compeed!!
Accessories:
Trekking poles are also a must and really help (particularly on the way down). A head torch is a really good idea as although you should never be walking too far at night, it is a key piece of kit. Also, get some iodine drops to purify water and anti-bacterial hand cleanser. Other than that, survival basics like a pen-knife, lighter, compass, whistle etc are a good idea. You should never have to use them, but it can't hurt to have them with you (and cause amazement among any Nepali children that you see along the way!)
How hard is it:
The short answer is very hard. I assume your trek will be around 15 days. The best way to prepare is to do what your doing. Go walking for long distances and take a heavy pack on your shoulders. In reality, porters will probably carry most of your gear, but without altitude to train at, a heavy pack is a good way to condition yourself.
Altitude :
1. Go slowly - I can't emphasise that enough - every breath you take at a lower altitude on the way up will help you to acclimatise. Don't feel pressured to walk anywhere fast. The slower you go, the better your chances will be!
2. Trek high, sleep low - This is followed in the Himalayas almost always, try to sleep lower than your maximum altitude each day
3. 300m a day - Try not to exceed climbing more than 300m a day in terms of sleeping locations
4. Keep your guide informed - If you don't feel great, let your guide know. They will all be well versed in the symptoms of AMS, but it can't hurt to have a professional watching your back
5. Diamox - Really controversial one this. You can buy it in almost any Kathmandu pharmacy and, as you probably know, it is designed to combat AMS. The key is, never self prescribe it! Have it with you, but if you need to take it, that should mean end of trek and descend. If you feel that bad, let your guide know, tell him that you want to take Diamox and get his opinion. If you take it too soon, it won't work, and if you get worse, it will have no effect.
I don't know anyone who hasn't suffered from the altitude (apart from the Sherpas!) You will feel it and parts of the trek will be very hard - but the end goal is worth it! :-)
How to get the most out of it:
It still is the most amazing place I've been or thing I have done. Much more enjoyable than Kilimanjaro or any other trek! The landscapes that you go through are breathtaking, from rivers and villages near Lukla, to the rocks above the treeline. The people that live there are by and large buddhist, and you will see the 'eyes of the buddha' looking at you from the 'Stupas' along the way. The mountain views are amazing and the stars are breathtaking. As hard as the trek can be at times, especially the altitude, the scenery is astonishing and certainly adds motivation when it gets tough.
As for the people, the sherpas are great. Really fun and unbelievalbe climbers (all about 5 foot and will overtake you on the route with fridges on thier head - literally fridges!) A deck of cards is often a good idea as the Sherpas love to learn games etc.
All in all I'm jealous! You'll have an amazing time! Nepal is a great country and the trek is phenomenal. Good luck and good luck with the record (I think a shortened run up might be an idea!)
Apologies if I have rambled too much above!