To really stretch a modern computer, you need something like a an interactive shoot'em up game. As these are popular with the yoof, even basic machines these days have enough grunt to do 3D CAD. It just has to be reasonably modern. Unless you go deliberately down market with a tablet, or a very cheap laptop, secondhand, or use a server, you will get a moderately fast multi-core processor with at least 4Gb of memory, and – most important – a recent Graphics Processing Unit (GPU).
A GPU is an interesting beast. It provides massive parallel processing for graphics that can be tapped into by anything needing serious mathematical grunt in the way of matrix manipulations. Like 3D CAD with Finite Element Analysis.
My experience with Fusion360 on Windows 10 is probably typical of what might be expected of Alibre. Fusion runs satisfactorily on an ordinary 3 year old 64 bit 4-core mid-range laptop with a hard disk. It's a genteel home-office machine, not a hot multi-media or games box. Fusion tells me the laptop's bog-standard built-in Intel graphics card (with GPU) isn't optimum, but everything works. I've animated a couple of simple engines (100 odd parts and joints) with no sign of slowing down, though the cooling fan gets busy! The laptop's a bit sluggish, not bad enough to annoy, and I use it a lot while watching TV with my daughter. (She makes me watch terrible telly.)
However, Fusion feels far more slick on a 4 year old 8-core mid-range workstation with an SSD & 8Gb memory. The really significant difference though is the workstation's big screen: I'd recommend buying one for any serious work on a computer. Doing CAD on a small screen is a bit like modelling through a letter-box.
Graphics is one of those areas in electronics that advance rapidly every few years . Unfortunately the advances rely on lots of fast memory and up-to-date hardware. In that context 32-bit and XP aren't 'reasonably modern'. I'm afraid if you want to do 2018 CAD, an upgrade may be necessary if you own an old computer. You have my sympathy, I found converting to Windows 10 irritating because I had to switch off unwanted new features that intrude on my privacy. Apart from that it's OK.
Dave