well, I think you HAVE enough budget for a tower (with your next paycheck, possibly some savings). For your budget, I don't see you getting a very "well spent money on laptop".
bottom line...
Skyrim is pretty dated, yes I know you said about mods but the game is still aged. This makes it easier for a system to run it, meaning that you will not need to max everything out if you know what i mean.
well lets just show this, this is a very ROUGH .. mostly "price" reference list, I went very quickly with it. You can get a very nice PC for that amount of cash.
basically i5-7500, enough ram, decent GPU, OS, Monitor. (didn't select keyboard/mouse)
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-7500 3.4GHz Quad-Core Processor ($198.88 @ OutletPC)
CPU Cooler: Cooler Master Hyper T2 54.8 CFM Sleeve Bearing CPU Cooler ($14.89 @ OutletPC)
Motherboard: Asus PRIME B250M-A Micro ATX LGA1151 Motherboard ($84.99 @ SuperBiiz)
Memory: G.Skill Ripjaws 4 Series 16GB (2 x 8GB) DDR4-3000 Memory ($89.99 @ Newegg)
Storage: ADATA Premier SP550 240GB 2.5" Solid State Drive ($69.99 @ NCIX US)
Video Card: MSI GeForce GTX 1060 3GB 3GB GT OC Video Card ($208.99 @ SuperBiiz)
Case: Fractal Design Define S ATX Mid Tower Case ($57.99 @ NCIX US)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($43.75 @ OutletPC)
Operating System: Microsoft Windows 10 Home OEM 64-bit ($88.58 @ OutletPC)
Monitor: AOC i2267Fw 22.0" 1920x1080 60Hz Monitor ($90.98 @ Newegg)
Total: $949.03
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-01-26 22:27 EST-0500