About any new Windows machine would work.
I recommend a minimum 8Gig of RAM.
I recommend a minimum 17" screen with a full numeric keypad for doing CAD work.
As the spec's JD posted, a decent graphics card. Look for a "Gamming" type machine as they tend to have better graphics cards.
as has been mentioned, a gaming laptop as a good start.
try to get a 1080 screen as a 720 screen is under the minimum resolution for Inventor. A smaller resolution will mean a (much) smaller working area plus, in the past (think most have been fixed now) some options screens are longer than 720 pixels and thus the OK/Cancel buttons are off the bottom of the screen.
make sure it has a dedicated graphics card...
You mentioned £ so I'm guess you're in UK. Check out the Dell outlet for cheap laptops, their XPS range are usually pretty decent for gaming, but I have not personally tried them with Inventor for years.
Ram is cheap, so if you find a good deal with everything you want but only 4Gb ram then get it and upgrade that yourself - this is what I did from the Dell outlet years ago. Got a laptop with an rrp of £1300 from the outlet for only £450 but it only had 4Gb ram, so for £35 I got an 8Gb kit and swapped them.
In all honesty, £500 might be a little too low - possibly ok with smaller assemblies but you might need a slightly higher spec for large assemblies and complex parts using lots of surfaces.
Sam M.
Inventor and Showcase monkey
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Have a look at this link for the System Requirements: http://knowledge.autodesk.com/search-result/caas/CloudHelp/cloudhelp/ENU/FlowDesign/files/GUID-F3997...
I have a Dell Inspiron 17. Have a look at that, It is working great. It has 2 different Graphics cards. One for High Performance like my Inventor software and one for everyday tasks like Emails. I havent had any problems with it.
I am not sure what your price conversion is currently but I paid R16000 for mine. Go have a look at it or something similar. But like JD said. Lots of RAM and a good graphics card
I have an 8GB Windows 7 Fujitsu machine with a full keyboard with numeric pad.
The processor is an Interl i5 2.6GHz.
Slightly slow with Inventor, but decent.