Here's the website
https://www.westhighlandway.org/Campsites generally have showers. Some will have somewhere on site to get food, others are close enough to villages with pubs that you can easily get hot food.
Budget of £700 inc. food is do-able, but it depends on what choices you make. It works out at £100/night. If you get a pub meal and drink every night, that's probably going to work out at around £15/head, which for a family of 4 is £60 leaving only £40 for accommodation and your other two meals. If, on the other hand, you take dehydrated food or buy ingredients in a local shop and cook your own meals some nights that's going to leave money in the budget.
Similarly, B&B's will be more expensive than bunkhouses or hostels.
Footwear is a perennial discussion. The route is mostly well-made paths, so you should be OK in trail shoes, although some people prefer boots.