The argos one does look ok, even though its a HDD. If you're used to a hard drive it shouldn't be too significant.
To be honest though, windows only takes about 30 GB so that gives you around 85 GB left on the amazon laptop I showed you, that could be usable if just for work, pushing it though. If you did need to, you could get an external hard drive later down the road or upgrade the internal drive (pretty sure that would void your warranty though).
If you intend on gaming then you would probably need more space, but the sort of games you could play at this budget probably wouldn't take up too much space. If you look at the min requirements for the games you want to play, like for Sims you could just check on steam. You should be fine but the graphics card (which is integrated) would really be pushing it and to be honest I don't really know as i'm not too familiar with integrated graphics for gaming. Otherwise the specs are fine.
So I would probably go for the Asus from amazon or the Argos one (the Amazon one you sent looks like its used, if you're not up for a refurbished laptop not sure if you'd like that).