People are recommending some nice stuff, but it's easy to get going with really no budget. I started taking photos last summer. Basically all you need is a camera that you feel excited to take photos with and has enough tools to be useful. I picked up a Canon T5i (circa like 2013) with its kit lens (18-55mm) and a zoon lens (55-250mm) on eBay for like $350. Then I picked up a 10-20mm wide angle lens for like $100. That's less than $500 in with a full range of decent enough (for a starter) lenses. Most everything I've taken (here's my page: https://500px.com/mycolorblindeye) has been with this camera and lens setup, though I swapped the 18-55mm and 55-250mm for a 18-250mm lens so as to save space in my bag.
That being said, I'm currently lusting over the Olympus PEN-F, and it's little brother, the PEN-E PL7. The PL7 comes in new around $600 and its reviews are really strong overall. These cameras are both micro 4/3 lenses so you have a great selection of glass. Probably worth a look in your case, as it's right in your price range.
Here's my general new photographer advice to consider (taken from another post of mine, so not necessarily specific to your case).
1) Pick a camera body that will allow you to gradually grow your lens collection. You're going to want to buy fancier lenses as you get into this hobby more. Lenses are more important than your camera body for creating a high quality photo. However, you'll want to be able to upgrade your camera body at some point when you hit a point of diminishing returns. So if you buy $500 worth of Canon stuff to start, then add another $1500 worth of lenses over the next 2 years and you decide to upgrade your camera body to another Canon, then it works out great because you have this catalog of lenses you've bought. However, if you decide to switch to Sony or Nikon or whatever when you upgrade then you're going to be purchasing a newer, nicer camera body which is expensive, but you'll also have to re-purchase all those lenses for your new camera. This is one reason why micro 4/3 is a nice ecosystem. There are two brands that make camera bodies and lenses, and then there are also 3rd party lens manufacturers, so your options stay pretty open.
2) Realize that a better camera won't make you a better photographer. Buy a decent camera but don't break the bank too much. There are tons of videos on YouTube (one example here: https://youtu.be/uv0n52-ncmg) of people taking great photos with absolutely shit cameras. If your photos look bad then you need to work on your skill at taking and processing them, but don't just pour money into a higher quality rig.
3) Speaking of processing, learn it! Adobe Lightroom is easy to use and is absolutely key in creating nice photos. Simple touched to color grading, contrast, etc. can take a photo from meh to fantastic! Also, if you want to get into black-and-white photography, you'll need this. The software looks daunting at first but you can gain proficiency in just a couple hours.
4) And on learning how to take the shots themselves, there are great communities everywhere, but I suggest using http://www.r-photoclass.com/. That website is basically an archive and continuation of the Reddit r/photoclass page that they did one year. It has archives of all the lessons they did, and it's a great tool to help you learn the basics and then enable you to go a bit further. It also talks about basic post-processing, so you'll have guidance as you learn that bit.
5) Back to camera purchasing advice (who said this list had to be a logical order?). But something you'll want to carry on a daily basis. I have my DSLR and 3 lenses that bounce around by bag all day. They're heavy as shit. I carry them because I love them. That being said, many people will hate lugging the extra weight around. If that sounds like you, you might lean toward the micro 4/3 system as a way to save on space and weight so you can carry your camera around on the daily. When you start taking photos, you'll notice that landscapes, architecture, and street scenes start to stand out to you as photo-worthy. In those moments, not having your camera on hand can be torturous.
6) Accessories. The basics. a) Buy a tripod of some kind. I snagged a GorillaPod and a cheap full-size tripod. b) SD cards. At least 32GB. You don't want to have to pull you photos off every 3 days. c) Long-term storage. I'm a fan of never deleting anything ever. Consider getting some external hard drives dedicated to your photos or budgeting a Google Drive subscription into your plan. If you already have a NAS setup then you're lucky and I envy you. d) Don't buy any filters or other semi-gimmicky items until you've found out that there are times you need them. Stuff like that is a money-pit for beginners. e) Buy a camera strap that isn't the one your camera comes with. We get it, every person who lives in NYC: you spent like $4000 on your Canon 5D. You know why I know this? Because you're wearing your camera around your neck and when I'm walking behind you your camera strap says "CANON EOS 5D MKIII" in bold letters across the back of your neck. Pet peeve of mine, but it's just begging for someone to steal you camera, and it's sort of obnoxious. Snag a comfortable adjustable strap so you can keep your camera accessible and secure on a daily basis when you're out and about.
7) Last piece of advice. Use https://www.dxomark.com/ to help inform purchasing decision. They have maps showing clarity and degradation for cameras and lenses of all kinds, as well as pretty informed reviews that come from as objective a perspective as possible. It's a great resource for buying bodies and lenses.
