It would usually be less hassle to go back to the original solicitor, but this is not always the case. If:
1. He\she still has your deeds (which would certainly be the case if you bought within the past two months, and could be the case for anything up to two or three years)
2. The title is unusually complex (unusual in a rural or suburban housing estate, could happen easy enough in an inner city development)
then clearly he\she would be in a better position to deal with the matter.
However, if your deeds are already sitting in your bank, and if it is a straightforward title, such as a Land Registry Folio, and an unmodified (from new) estate type house, then any solicitor should be happy to take it on, and the original solicitor is at a relatively slight advantage in terms of familiarity with the papers. Indeed, if the original transaction was more than 12 years ago, your old file might be gone to the shredder by now, so I am afraid the answer is really that it depends.
As to price, I think that that something in the region €500 - €650 plus V.A.T. (21%) plus outlays is achievable at the price-competitive end of the legal market. Anything more than about €1,200 plus V.A.T and outlays would be a bit top-heavy for a straightforward re-mortgage file, unless the circumstances are unusual.
Incidentally, when I refer to a straightforward re-mortgage file, what I mean is that you do not absolutely have to have your solicitor phoning and writing to the valuer, the life insurance people, the building insurance people, the management compant people, your architect, your credit union, your car loan company etc. Many solicitors who do all of this stuff reflect this in their fees. Conversely, many "cut price" solicitors will simply prepare the legal papers, submit them to the lender and then notify you of what you need to sort out before the loan cheque can issue (which is absolutely fine for many clients - and logically there is no reason you should pay a solicitor to do things that you can do yourself, even though many people make exactly that choice).
While paying extra certainly isn't a guarantee of a higher level of service, and while keen fees do not necessarily mean low service, problems usually arise when the solicitor and the client have differing expectations. For this reason, and a host of others, I always maintain that it is best to use a solicitor who comes recommended, rather than saving some small few euro with someone who you know little or nothing about.
hope this helps.