You don't need necessarily need to wear a suit, but you should go dressed smart, first impressions count. It would also be useful to bring any relevant qualifications down with you and also things like driving license and counterpart, NHS no. and passport. Inaddition, do some background work on the unit your interested in, look at the army website and get some info.
Whilst working in AFCO's I've come across many admin nightmares so when your recruiter tells you that you'll need something, make a note of it and get on it. Your side of the application process can be speeded up if you go 'switched on', then it just depends on medical dates and if you need vetting or not, which the recruiter deals with. Alternatively, don't bring whats required of you, don't turn up on time and be a mong in the system for up to a year.
Also if you have any problems with the application itself like a particular question, make sure to contact you recruiter, nothing worse than having to constantly dish out new bits of paperwork.
try and get a contact number for the unit you have your eye on, best to phone in advance because the relevant recruiting staff may not be in when you plan to visit, so best to check. That is the first and only step. The staff will do the rest and explain everything you need to know!