Tablets: some can connect directly to 3G/4G services (about £100 extra). Most of the good ones have GPS, accelerometers and really decent cameras (video and stills), but basically most of the *portable* functionality of a laptop can be done just as well on a tablet. They don't run Windows which is *probably* a security advantage. Applications are *much* cheaper.
If you use Android, you can connect external keyboards and mice (Bluetooth), and get at files easily to and from a PC. It's not quite so easy on an iPad, as the operating system pretends it doesn't understand the idea of a 'file' and complicates matters, but a standard Apple Bluetooth keyboard works pretty well (actually slightly better on my Android one!).
iPads, Samsung Galaxy Note and Tab, and Google Nexus tablets all have very good screens indeed, with better-than-HDTV quality. I watch the Grands Prix on my Galaxy Note 10.1 (or her iPad) and can watch in HD (depends on the connection). There's enough storage for several films, and bucketloads of music if you want.
The Galaxy Note has infra red, meaning it can work as a TV remote control (annoys the kids, that).
I use Direct Office Print (on the Android) meaning I can print to pretty much any printer that's visible on the network. It's available for the iPad too, I think, and works fairly well.
Both have quite long battery life - about three days irregular use or four to five hours continuous. Mine uses about 25% of the battery on a 1 1/2 our Grand Prix highlights programme.
The Android does handwriting recognition really well (good enough to use for real work), and the stylus is great. I use a graphics tablet instead of a mouse on the PC so I'm used to them, and I find it fast. Only drawback is that it makes poor use of the button on the side, but that's just poor coding.
Almost forgot Dropbox and Google Drive, for moving files into the 'cloud' and back to a PC or Tablet. Basic storage is free, and it works.
They're not a replacement for the main home PC. I'd say laptops aren't either, but many people do that nowadays, so I'm outnumbered there. But having had one since Christmas and used it for work as well as play, I'm not going back to a laptop unless there's a really compelling reason.
If you do get a laptop, have a look at Asus. they aren't that well known as a brand, but the company makes for many of the big names, including Apple HP, IBM, Dell and some others, I think. I've always found their lower-spec machines to be exceptionally good value (bought two in the past), and they're very compatible with few oddities.
Also checkout offers on sites like scan.co.uk. I've bought from them on and off for about 15 years - thr Today Only offers can be pretty good value, sometimes including laptops.
Stay away from cheap Android tablets though - mainstream brands only. Samsung and Google Nexus have the best support, for applications and problem-free operating systems. Some of the cheapies are rough round the edges and aren't worth it.