You can blow a lot of money with a case. If you're in the states, there are some budget options from Rosewill
and DIY PC
available on Newegg that aren't top-tier, but have nice features and are a good case for the money. And there is usually free shipping involved (keep an eye out on spotlight deals and email specials). Deepcool
is another one that seems decent for the price.
I personally have an LGA 1150 premium Asus board with a 3550k i5 in there. These were bought a few years ago, and packed up shortly after being built for reasons I won't go into. They're still essentially new with only a few hundred hours on the components before being unpacked recently. It's got 32gb ram (way overkill) and a recently-added 6gb MSI GTX 1060.
The 1060 is a rather unique card, as it is an extremely low-power PSU that can be ran off of a 400 watt power supply without issue. It's powerful, allowing for VR and hardware encode/decode of 12-bit hevc (x265), which is important to me. It supports 4k video without issue, and its the best card for the dollar value at 1080p resolutions. The MSI version that I've linked is awesome... it's a very slight step below EVGA's best offerings, but at a steep discount from EVGA's price, and with much better features (EVGA doesn't provide a backplate) - note that I don't care about lighting, but my MSI offers that. EVGA doesn't. It's also a slight step below the Asus STRIX card (ie this is the 3rd best GTX 1060 currently on the market) - but the margin between #1 and #3 are very slight. The price differential between either of the others and the MSI made up my mind (I got mine on pre-Christmas winter sale for $234.99 after MIR, which has already been received). Do note, however, that the 1060 is NOT capable of running SLI.
All in all, with a ~$60 PC case, $80 2tb Seagate HD, ~$275 video card, and ~$80 16gb ram, you've plenty left in your budget for a decent i5 cpu/mobo combo, especially if you look at a new or used previous generation chip. Or you could go new and get the best combo that your remaining ~$300 will purchase, which shouldn't be too bad of a system, but not premium/gamer level.
I can tell you that I max settings with Arkham Knight on my setup at 1900x1200 and have noticed no issues. If I were building a mid-budget PC build today as you're trying to do, I would search out a near top-tier previous-gen mobo with an unlocked CPU and go to town. Disclaimer - I don't have a need to constantly upgrade and don't plan on gaming at 4k resolutions or with dual monitors. I also don't need to have every game I play set with maxed-out video settings, so SLI has never been something that I've needed. For me and my habits, this style setup will last me for several years, properly cared for. And it fit my budget (~$700 a few years ago, all new components, including a $150 top-tier Cooler Master gaming case and ~$250 recently to bring it to modern gaming spec, as the previous video card I had in there just wasn't cutting it)