If you don't want to take a suitcase on day one I know some people will bring a large rucksack with space for enough uniform for the next day, and then make a decision whether to ferry it home over the course of a week or bring a large case in the next day, or indeed take the large box home. In my day you got two boxes and it was before training commenced, and whilst awkward I was able to get them home to Derby, where I was living at the time.
For the person asking about dress code for day one - 'smart business' is the usual term used. A plain t-shirt and smart, dark jeans would be acceptable for one day (albeit right on the edge of the dress code) but light jeans or a graphic t-shirt wouldn't, nor would tracksuit bottoms. Ultimately: it's your first day at a new job, and you want to make a good first impression. A full suit is overkill, but there is a need to be 'presentable'. Equally - for one day only you won't get too much grief, provided it is work appropriate.