[MENTION=19649]elninobonito[/MENTION] Las Vegas 10k sounds like fun - a bit hot and sticky though, in my experience of Vegas! I'm not sure where you could go for specialist advice in Crawley, but I know they have both a Decathlon and a Sports Direct. I would try on as many shoes as you can bear to and see how they feel - it was my experience at the start of my running interest that trying a few different types of shoe was crucial. You eventually find what you like and that's when its worth investing the cash money. I'm a big fan of Asics footwear, all my running shoes are Asics.
The LV 10k iirc is run in November, it isn’t that hot then, today highs of 13c as an example.