From my experience some alcohol goes down well with most teachers. We moved three years ago so moved schools and the first year at this primary we bought 6 bottles of wine - 2 white, 2 red, 2 rose and a couple of bottles of Shloer - and just went around the boys' teachers and TAs and got them to choose which one they wanted. They all seemed very happy with that option and we were left with the Shloer, happy about that as we don't get through much wine, prefer vodka.
We only have one child left at primary now but weren't sure what to get his teacher this year, she has only been here the one year and didn't know her. Was thinking some pens/pencils/glue sticks/nice notepad etc to help finance next year but didn't know what she liked for something for a little treat for herself. Ds suggested a box of chocs, also thought about wine, flowers etc. Asked another teacher and she confirmed ds's teacher likes chocs, prosecco, sweets in general and has a sweet tooth so cakes as well. (I also said we didn't want to lumber her with a mug saying 'World's best teacher' as it would probably just join with a dozen more at the back of the cupboard, teacher agreed.)
Ended up getting a pack of pencils with rubber, sharpener etc and a mixed pack of biros 'for later' (thinking it would be something she didn't need to buy herself for her new school in September) and a smallish box of chocs and a smallish bottle of prosecco 'for tonight'.
She opened them during the day and started eating the chocs during the day, didn't start the prosecco until lunch time, I guess was saved for after school, but she was rather pleased with the biros! She couldn't find any of her green biros for marking and opened the pack there and then to mark the children's work before they left for the summer! So we think everything was appreciated.
But we are the kind of people who prefer to get two or three little things when it comes to going to class birthday parties, this way there is a chance the child will like at least one thing they get from us. So instead of buying a jigsaw or a nerf gun that is the full price of our budget we might get some play doh, a small jigsaw/board game and some sweets. The last party ds went to was a nerf gun party so couldn't even buy one for the birthday boy then as he already had about a dozen so he got something to do with Spider-Man, sweets and some glow-in-the-dark putty. If we don't know what people like we try to get a selection so they can hopefully keep something and swap the rest with someone who wants them.