There are 2 occasions when I would recommend a laptop over a PC. (i) If you really need your computer to be portable or (ii) if space is a real issue.
Otherwise get a desktop. These are reasons why:
1) Laptops are more fragile & far more likely to get damaged. Because they are portable there's a higher risk of them being dropped, or stepped on or damaged in some other way.
2) When they do break, they're much harder & much more expensive to repair. A replacement screen for example (often the first thing to break when a laptop is dropped or stepped on) will cost you in the region of £200 upwards including labour costs). A replacement motherboard will often cost £200 - £300 (for a new board & labour). You get the idea...
3) Laptops are less upgradeable
4) Laptops are often harder to type on because of the condensed keyboard layout etc
5) Laptops are more likely to overheat under load & have limited cooling upgrade options
As for brands/companies etc, it depends on what you want. Dell, Acer & Sony are normally OK, HP/Compaq are ok-ish, and I wouldn't touch eMachines, Packard Bell or eisystems with a 10ft barge pole. If you do want a laptop, then Acer & Toshiba are usually fine. IBM are fantastic but expensive and Lenovo were great until they started manufacturing them in China.
If you're looking for something other than the big name brands, then I've heard very good things about Novatech (assuming you're in the UK). If you 're in the States, then I can't help you.
Hope this helps a little