I'd ring the centre where you are going to have the lessons and ask what their dress code is.
Wearing a tie sounds a bit over the top to me and would have thought a smart polo shirt would be good enough (not in lurid colours though of course !).
Enjoy your lessons - it is a great present and better than a lot of the ones i've ever had.
lol - i wear some weird colours myself if hacking. But if i was turning up for a lesson at a place i'd never been before then I would tend toward a bit conservative as people do make first impression judgements and lurid neon yellow and pink can be a bit off putting. Especially if you want relatives to take pictures and you are given a chestnut to ride. But that's just my opinion.
I was schooling my fluo chestnut mare today in dark red jeans and a hi vis yellow t-shirt. I probably wouldn't choose that combination to get photos, but I have no qualms about tuning up wearing it in public either
It sounds like it's your first lesson so I wouldn't worry about being in a shirt and tie. If it's soon and its still hot a long sleeved plain top or a polo shirt would be completely appropriate everywhere I've ever ridden. I'd avoid strappy tops or any fashion clothing (i.e slightly longer tops - you'll end up sat on them!). If you need a jacket then something that hasnt got straps and you can move easily in. Being able to move easily and feeling comfortable is the most important thing!
My advice when answering this question at our riding school is: be comfortable, so I suggest leggings/jeggins or running tights, polo shirt or t-shirt with sleeves, and if you have boots with a low heel and no zips on the inside of the leg, that is great. We will lend hats and boots for the first few lessons.
Please, just phone the riding school and ask what they would prefer. Honestly, they are used to the question: it's much easier for them if somebody has asked the question rather than turning up in inappropriate and dangerous clothing.
if you team those with a boot with no zips and a short heel and running tights then you will be comfortable. Any T shirt and sweat shirt that is relatively plain and without excess bobbles etc would be great.