What size case are you looking at? Slimline like a dvd player, a cuboid shuttle case, or a standard pc case with a cutdown height or one thats designed to look good while lying flat? Any cases that are less than 13cm in height need low profile components, which is something to bear in mind, though there is no problem in getting tv tuners that size, and you will only be needing onboard graphics for dvd resolution anyway.
As for how it looks on the tv screen, video will look fine on a standard crt tv, but text is a no go, easily readable on lcd screens but looks fuzzy on normal tvs, because a standard tv has a low res, you dont want to be increasing the font size either because then you will be scrolling a lot. 10cm high micro atx slimline(ish) cases are about £30, shuttles are about £100 (socket A) which includes the power supply and motherboard and the standing micro atx cases are £20 upwards. Its also possible to get 5cm high ones, but I wouldn't reccomend that to someone who hasnt had experience building small pcs.
You may need to spend a fair bit of money £50-60) on quiet cooling and a silent power supply if the noise would bother them, generic crap is usually about 30db, with better stuff being about 20db. Your pc would probably need about a 2.0ghz cpu with 512mb ram, hard drive size depends on how much you want to be able to fit on it (you halve the hdd size to work out how many hours you can fit on it), 80gb will probably be more than sufficent. A decent digital tv tuner will cost about £40 (id reccomend the compro dvb-t 200), and if you want a small case youll need a micro atx motherboard.
And then theres extra things such as dvd-rws if you want one. You'll need to buy some cables and possibly adaptors to connect it to your pc to your tv. Also youll need a copy of windows media centre edition to be able to use it simply and have a proper home entertainment system look. This costs about £80 on the internet, though of course you may have your other "sources".
AMD Sempron 64 2600+ 1.6GHz (Socket 754) CPU - Retail
£39.95
Abit KV-85 VIA K8M800 Micro ATX (Socket 754) Motherboard
£39.95
OcUK Value 512MB PC3200 184pin DDR Memory
£21.95
Maxtor DiamondMax Plus 10 NCQ 80GB 6L080M0 SATA 8MB Cache
£33.95
Sony DDU1613 DVD-ROM (Silver) - OEM
£12.50
Tagan TG330-U01 330W ATX Silent PSU
£27.95
Zalman CNPS7000B-ALCU Ultra-Quiet CPU Cooler - Retail
£15.95
Compro VideoMate DVB-T200 Digital TV Internal PCI - Retail
£34.95
Subtotal £227.15
VAT £39.76
Total £266.91
Your looking at around that price plus, your choice of case (unless it's barebones which will come with the mobo and power supply), and about £10-15 for cabling, depending on what connections your tv has and if you need any adaptors.
With sky plus you could record of 2 channels at once, but it costs £120 a year for it, and it isnt as featured as a pc is.
Edit - Is it just me or have multiple posts in this thread dissapeared, ive got subscription emails with replies in but none of them are here? Probably a forum error or something.