The first thing I can say is you 100% need a GPU. My laptop is pretty much unusable for GameDev as it stands, it's a simple i5 + 6GB Ram, but it's pretty slow in comparison to my desktop and there's a lot of idle time wasted. I also cannot test certain things in my game, and have to run it in low settings just to get it open. Whilst it is good for testing on the lowest end of machines I end up targetting, and has a decent processor, the lack of GPU just makes it hard to work with.
A few comments i'd make:
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SCREEN: 1080p screen is pretty essential IMO, unless you have access to a 2nd monitor (1366x768 is a very poor amount of screen real-estate and you'll find it hard to have multiple code windows open) -- I used to use my laptop in school and would often just borrow a monitor from one of the desktops when i used it
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GRAPHICS CARD: Defo get a GPU, doesn't necessarily have to be a really good one, just atleast you have something that can offload the work from the CPU and allows you to do some level of graphical testing without pooping itself.
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SIZE: Get a full size laptop (15.6" atleast). From years of working for the University Student IT support service, so many people would come in with seemingly decent spec laptops (i7 + SSD), but they would perform like potatoes as they were small and thus the processor speed was throttled to 2.0GHz or there abouts to prevent overheating.
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STORAGE: SSDs are nice, but not essential. I'd get one if you find a good deal (i'd sacrifice getting a worse GPU over a better one if an SSD came in the package). Whilst it's not essential, it improves the speed of everything (compiling, loading etc) and just makes it feel more responsive. (If you do, capacity should be atleast 256GB as a lot of laptops don't come with secondary HDDs, and anything less will fill up very very quickly).
- Don't bother with any fancy touch screen or gimmick features, these just inflate the cost and mean you are getting a less powerful machine for the same price
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PROCESSOR: Getting atleast an i5 (or AMD equivalent) is a good idea. Anything less will likely only have dual core and ideally you want atleast 4 cores for game development.
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RAM: I'd suggest atleast 8GB. 6 is probably the minimum amount you'd want if you have other programs open at the same time as GM.
- I'd recommend spending atleast £800 (or your regional equivalent ~$1000 USD). This is quite a lot, however I think that's the minimum you would want to spend if you want to avoid development efficiency hurdles.
If you want a machine more tailored to gaming, then ignore what I said about preferring an SSD and get a better GPU instead (if you are on a budget).
An min-spec for a general development machine:
GPU: GTx950, GTx1050 equiv
CPU: Intel i5
RAM: 8GB
STORAGE: 256GB SSD
SCREEN: 1080p
Gaming spec
GPU: GTx960+
CPU: Intel i5
RAM: 8GB
STORAGE: 1TB HDD
SCREEN: 1080p
Some really good deals I found (UK links, but models may exist elsewhere -- Price conversions done factoring in the fact that computer tech is always about 10-15% cheaper in the US, even after currency conversion):
https://www.amazon.co.uk/HP-Pavilion-15-bc006na-15-6-Inch-Natural/dp/B01H9UVTW6/ref=sr_1_2?s=computers&ie=UTF8&qid=1510448056&sr=1-2&keywords=laptop&refinements=p_n_feature_browse-bin:1481781031,p_n_feature_keywords_browse-bin:2989741031
(This machine is a bargain, i5, GTx960M, 8GB Ram, 1TB HDD, 128GB SSD @ £721.98 ($920)
https://www.amazon.co.uk/Acer-VN7-591G-15-6-inch-Notebook-Resolution/dp/B00YRY9AP6/ref=sr_1_8?s=computers&ie=UTF8&qid=1510448056&sr=1-8&keywords=laptop&refinements=p_n_feature_browse-bin:1481781031,p_n_feature_keywords_browse-bin:2989741031
(i5 CPU, 8GB Ram, 2TB HDD, GTx960M @ £687.13 ($880)