In Australia half chaps are fine too, as long as they are leather. :)
An all purpose saddle will be fine to use at lower levels for both the dressage and jumping phases. Heck, I even show jumped and went XC in my dressage saddle on my TB as it's the only saddle he has. :)
As albertaeventer said, any horse can event, we have warmbloods, TB's, riding ponies, arabs, shetlands etc going round over here.
Your arab will be fine. My eventer that I have been telling you about is a 14.3hh Andalusian x TB x Riding Pony.
One of boss's TB's goes round Pre-Novice courses (which for us in Aus, is just below 1*) with only front shoes... and no stud holes. He has never had a problem with lack of footing.
Not sure how you go for prices over there, but over here my expenses are as follows (all in AUD);
Entry + Fees - $100-$120
Petrol/Gas - $70 for a tank
Yards/stables - $0 as I use my portable float yards
Food for the weekend - $50 we take eskis and stoves and cook up our own food.
Camping - $0 as I roll out a swag and sleep in the back of my float, after it has been cleaned out :)
This website is pretty handy too... http://e-venting.co.uk/?cat=13&paged=2