Welcome, Byte!
That's a ridiculously great price for a new Tamagotchi, and especially for a vintage. As your P1 came with its original packaging, you probably have the instructions which should give you most of the info you need. The Original Tamagotchi is very systematic so chances are events will repeat a few hours after each other, such as calling for discipline or going to the bathroom. If you don't have time to take care of your Tamagotchi, you can pause it by going to the clock screen and pressing and hold A and C to put the clock in set mode. While in set mode, the tamagotchi will be in limbo and not grow or do anything till you set the time. A side effect of this is that changing the time will alter the tamagotchi's routine. For example, if you pause your Tamagotchi at 3 p.m. and then come back later and set the clock to 5:30 p.m., the tamagotchi will do each activity 2 hours and 30 minutes later than usual (such as calling for discipline at 6 p.m. instead of 4:30 like usual). This technique also works on any virtual pet (the collective term for pet-raising electronics) that allows the clock to be adjusted.
Vintage models - any Tamagotchi released in the late 90's - are raised from birth to death while all other Tamagotchis are raised from generation to generation, as they can produce offspring. Colour models are modern Tamagotchis that have a colour display and usually have tons of extra features compared to other kinds of Tamagotchis. They are usually in Japanese but can be patched to English, as well as have extra content transferred to them. The group of models that are not vintages or colours are connections, a reboot of the vintages released in 2004. These versions are characterized by their flat oval shape, curved infrared port at the top, and usually an antenna on the top also. Their display is usually black and white pixels like the vintage models, but some special versions have red or blue pixel instead. Connections are like vintage versions with more features such as being able to buy them toys, various kinds of food, play more games with them, and some can even have jobs. Both connections and colour models have the ability to connect to other compatible Tamagotchis to play games and visit each other, as well as marry and have offspring if they are the right combination.
Each specific model has its own little quirks so they should be looked up individually. The
Tamagotchi Wiki is a great place to look for information as is the TamaTalk forum. Additionally, there are many helpful youtube video for each model that you can find by searching up the model name. Chances are you'll find everything you need right on the forum just by searching a few key words. If not, we TamaTalkers will be happy to answer any of your questions