Grados are a very good suggestion. I use SR125s at home, but the open-back means they're not great for journeys. There are a couple of IEM Grado options; the older GR8s (£299rrp), the brand spanking new GR10s (£395rrp) or the entry-level iGis (£89.95rrp). I can't say I've tried any of the IEMs, but Grado are renowned for consistently awesome products, and if the over-ear iGrados are anything to go by, entry-level price does not mean entry-level performance. (The iGrados are a bit of a strange product to me - designed for portable use but extremely leaky, which seems to rule out a lot of their potential uses.)
For an amplifier, I don't think you can go wrong with the FiiO E7 - it's portable (rechargable via USB), drives an IEM like the iGis easily, and sounds fantastic. You can buy a dedicated line-out cable for iPhone as well, which will further enhance the sound, and the styling matches Apple products perfectly. It also functions as a USB DAC, meaning that if you want to listen to music from a PC/Laptop at a better quality, it'll help you out with that too - just plug it into your USB port and change the audio output in control panel on Windows. Link it up to the desktop Fiio E9 to drive some badass full size headphones like the Grado SR series and you'll really be laughing (I know I am, everytime I use it
). You can get the E7 for £47.44 on Amazon, E9 for £80.56, and the cable for iPhone connectivity for only a couple of quid.
For in the car, I'd say you won't do better than IEMs, as they help to block out extraneous noise, meaning you'll get the most out of the FiiO gear, and the headphones themselves. I use the FiiO E7 on the train with my iPod classic and Beyerdynamic DTX100s, currently on sale for £54.95 on hifiheadphones.co.uk, standard rrp £75.95. They're likely to be a close competitor to the Grados, but either way you'll be hearing some sweet sounds. You could easily set yourself up for under £150 for your purposes - if you're listening at home and want something full-size then adding in the FiiO E9 and getting a pair of the Grado SR80s or SR125s is the way to be comfier and hear even more. This is what I run, and on a student budget I managed to buy the whole rack in a year, and it's improved my listening experience immeasurably, especially when out and about.