Conveyancer might be cheaper but you'll get a better service with a solicitor (can only work for one side, must disclose any backhanders, probably has had more training/experience etc).
If you can get a recommended solicitor then go for them over a conveyancer, you might pay a few hundred quid more but it's worth it. I would recommend Glazer Delmar on North Cross Road, they're not the cheapest solicitors but they are very, very good. If your vendor on in the chain is using a crap conveyancer then a good solicitor can help.
I recently remortgaged and the mortgage company used Enact Conveyancing, they were utter rubbish and I even had to get compensation from them, the pointless delays they caused meant I was paying over the top on the mortgage. Do not use them, even though they might be cheap.
You may find your purchase goes though smoothly and you end up thinking, I could have saved ££££ using online cheap conveyancer but it's a gamble but as a first time buyer I think a solicitor would be best. Speak to 2 or 3 local solicitors, get a feel for them, recommendations if you can and choose one.
These might be useful:
] (a useful website for you and your questions :-) )
and good old Martin Lewis [www.moneysavingexpert.com