A common question this one, and I was here 2 years ago myself. Thought i'd share my experiences.
Generally speaking, buying a uke is like buying any musical instrument. Go too cheap and you will end up with something that may hinder your learning and put you off, not a good thing!
I appreciate however that not everyone has lots of cash, and certainly not cash to blow on something they are not sure of. Heck, ukes can cost more than £500 but how low can you go?
A quick search of eBay will show a variety of brightly coloured ukes in the £15 - £20 range. Do beware. I bought one of these and it really is pretty ropey.
Step up a level into the £30 £50 range, and you are in to the level that I would recommend for beginners who really can't spend much. Look for Makala ukes for example ( including the brilliant Dolphin series), or others from Makala. Bear in mind that these entry ukes won't be solid, and will definitely benefit from changing strings to aquilas ( so budget another £6 ). They may also need a tweak to set up such as slight lowering of action. This will be a breeze if you are a guitar nut, but complete newbies need to take care, take advice or possibly pay a luthier.
Moving up into the £50 - £100 bracket and you start to get more improvements in quality, and some solid woods. This is though the category to take care with. We are getting into more serious money, and sadly there are more bad ukes here that shouldn't in my view command higher prices. In my view look for Kala, lanikai, ohana and Baton Rouge. If you can reach 100, check out entry level Bruko. Great all solid handmade ukes! All ukes in this range may still need action checking and may benefit from better strings.
Up a step again into the £100 - £200 category and your choice widens considerably. I think this is the range where you really can get ALL the uke you need without going boutique / pro. All of my upper end ukes are in this range. Wooden ukes will tend to be all solid in this range, and whilst still made in Asia probably finished in USA, such as brilliant Mainlands. Very nice Kala and Ohana ukes in this range too as well as the standard model Fleas and Flukes ( everyone should own one! USA made)
Higher still and it's a case if 'where do you stop'. You are looking at upgraded versions of the above in fancy woods, or with pickups fitted, or into beautiful hand made Hawaiian instruments!
So, what did I do in the early days? Simple!
Mahalo - horrible horrible, sub 20- junk waste of money
Vintage - £20 - kinda junk, works, 'sort of'...
Lanikai - £50 - nice sound, stayed in tune, well set up.... Sold to fund...
Flea £120 - brilliant and unique, can't really go wrong
Bruko £100 - solid wood
Mainland £160 - concert scale, solid, beautiful, bought to compliment Flea with warmer tone and longer scale neck.
Beyond that I ended up with about 60 ukuleles at one point!
Hope this helps if you are confused. Email me if you have any questions. Above all, select a couple of models, research them ( ukulele underground site forum is your friend here) and try if you can to play them ( saying that, I never have myself!)
Good luck! Go buy one, you know you wanna!