Recommend Tyres for a Beginner

I have just got into mountain biking and have recently bought a Boardman Comp HT which is a great bike and as a beginner appears to tick all the boxes while at the same time will allow me to "grow into" the sport.

At the moment most of my cycling is fitness orientated with a mixture of roads, cyclepaths and blue routes however I am about to take the plunge with red routes and things a bit more technically challenging!

The one area where the Boardman appears to fall down would be the stock OEM tyres (Mountain Kings) which by all accounts are not very good in the wet and lack a degree of grip, I must admit they did feel a bit squirmy when I went out after the heavy rain yesterday, mostly on tarmac! Being a beginner, this has dented my confidence somewhat and I am wondering if it would be a good idea to upgrade the tyres. What I am after is a good all round tyre with plenty of confidence inspiring grip on the trail while at the same time doesn't compromise too much when used on the road, ie rolling resistance.

Also the stock tyres are 2.2 inch, using the same rims am I limited to this size or are other sizes an option? And is it worth just upgrading the front tyre? To my mind this would be the tyre most likely slip.

Thanks