What kind of desktop computer should I ask for, for Christmas?

Hi. I know that Christmas is still, like, 2 months away, but I'm already thinking of what to ask for. I already know I want a desktop - my current laptop is slow and useless. Also the battery is messed up because I didn't know not to charge it overnight.

Here are a few things I'm looking for -
1. Ability to do schoolwork. I'm a freshman in high school and have to type reports and do computer-based presentations, etc. There's also the typical need for internet surfing and research.
2. Mild gaming. Right now I'm interested in playing Minecraft. This would probably be one of the few games I play on it, along with a few casual games on the internet.
3. Speed. I'm so tired of my laptop XD. It takes forever to turn on, off, or load any websites. I did a Minecraft trial on it and that was a failure… I just want something that's fast.
4. Not too expensive. My family isn't the richest… I don't expect for my parents to spend any more than 500$ for the monitor and everything. And that's just a random estimate. It might even be only 300 or 400. So an option for this budget would be awesome!
5. Reliability. This will probably be the only new computer I get for a while… Or forever. I'm serious. So I need something that can last me, maybe until high school is over at least.
6. The space it takes up doesn't really matter… A thin monitor is preferable though.

Sorry this is so long! I don't know much about computers… Thanks for any help and ask any questions if needed!

General work isn't going to be a problem.

Minecraft I believe will run quite well on an AMD A-series processor, which includes decent integrated graphics. You can play other games on it but you'll have to turn down the details and/or resolution.

If you want speed and don't need much hard drive space (ie you don't have lots of music or videos on your hard drive) I'd look for an SSD (Solid State Drive), they're so much faster than regular hard drives. Unfortunately cheap desktops with SSD's aren't common.

That budget's tight especially considering you need a monitor in it. You'll probably have to compromise somewhere, maybe by only getting 4 or 6 GB of RAM. Check there are free slots for a future upgrade if you can.

Desktops are generally very reliable. I advise looking for something fairly standard - full size case, maybe from a smaller manufacturer that uses commodity parts. Compact PCs often use proprietary parts that are expensive to replace if they do break.

Charging your battery overnight was not a mistake. Li-Ion batteries have a circuit built into them to prevent overcharging. You can leave your laptop plugged in to power 24 hours a day without harming it. The way to damage a Li-Ion battery is to drain it completely. Each time you do, it causes progressive damage to the battery.