If it is at all possible, avoid a laptop or any sort of pre-built machine. You can build a PC very easily in an hour or two depending on how well you follow instructions. With a desk top that you build, any upgrades you might want or problems you might face are much easier to diagnose and solve without much down time depending on what the problem or upgrade is. Manufacturers of gaming computers simply can't afford to put in the level of capability that you get by building yourself for the same or near equal cost.
Step one is deciding how much space you have. There are three main sizes in the PC building library. ATX, being "standard" and fairly large. Micro ATX, what I would consider a "normal" sized PC in most cases. Mini ITX, which are small.
I personally run a Micro ATX build as I don't need a ton of PCI-E slots and only run a single graphics card. Most people with ATX builds have an over-sized and mostly empty case with the exception of the few who actually utilize the size ATX offers.
Mini ITX is likely going to continue gaining in popularity. My next build will very likely be a Mini ITX build because you can build an incredibly powerful PC into a case only slightly larger than your standard gaming console.
For a first time build, I'd grab a Micro ATX board. I am partial to intel. Their 8th gen stuff is fantastic, for a 1200 dollar build you should be able to afford an 8600k. That's going to be plenty for any game you wish to run.
Graphics card is important in many games, arma doesn't really utilize it as much as others so you could save some money there if you would like. I'd run a GTX 1060 for solid 1080p performance. Anything higher resolution and I would start looking at the 1070 or 1070TI.
Those two parts are the big expenses. You can save a considerable amount elsewhere if you shop wisely, and considering that cyber Monday is coming up you'll have the opportunity soon.
Don't go spending a ton of money on a case unless you have to and can afford to do so without cutting corners elsewhere. I like the simplicity and sleek looks of Fractal design, they have plenty of affordable offerings, second to them, I'd say CoolerMaster is one to look into. IMO, many other cases either lack ventilation, or cost more than I find reasonable. I like a quiet computer and don't run any lights nor do I have a see through panel. My build looks great when I pull the panel off, but I don't like hearing fans run. Fractal makes a very quiet case.
Motherboard would need to be a Z370 for the 8th gen intel. If you go 6th or 7th gen which are great and save some money, grab a Z270 as it will work with either generation and are still readily available.
Ram needs to be at least 8 gigs, preferably 16, at no less than 2400Mhz. Stick with a big brand and you'll be fine.
Power supply needs to be an EVGA for the sake of simplicity and reliability. Get at least a semi-modular with 650watt output. Trust me on the semi modular part. Otherwise you'll have a shit ton of cables that you have to stuff somewhere. There are many other brands but EVGA is known for great customer support, and if a power supply fries your build they'll more likely than not replace those parts fried if their PSU caused it.
At this point you're left with a CPU cooler and your storage. Any old 1TB HDD will do you fine for starters toss in an SSD no smaller than 120 gigs to store your OS on, and keep games on a separate drive.
CPU cooler can be a Coolermaster hyper 212 evo or a Cryorig H7. Both are great for the cost and keep your CPU nice and cool.
If you can't do a build for travel reasons or some other limitation, I understand, but if you could make it work it would change your gaming experience for the better without a doubt. I was on a laptop for a long time before making the switch and unless I was traveling constantly for work or something similar I could not imagine going back.