I'm surprised no one else has replied yet, but here are my views. Lots is my opinion, but it might help you get started.
I'm going to ignore interest-only mortgages, because I think they are hard to come by these days and I dislike them.
You can get fixed rates, discounted rates and tracker rates. You also have the lenders standard variable rate (or basal mortgage rate, or standard mortgage rate or whatever they decide to call it)
*Fixed rates are fixed, and the longer the term of the fix the higher the rate, but they do give assurance thet you will pay the same amount each month for the ficed term.
*Discounted rates are so many percent points below the lenders standard variable rate. They change as the lender changes its default rate.
*Tracker rates do not depend on the whim of the lender, but on the Bank of England Base Rate. They will be so many percentage points above the BoE base rate (in the past, they could have been below the base rate, but you won't get that at the moment).
Most lenders change their own variable rates in response to the Bank of England rate, but it isn't a directly proportional change. When the Bank of England rate was high, lenders standard variable rates were a couple of percentage points below it. Now that the Bank of England rate is so low, lenders are typically 4-5% above it. The difference between Discounted and Tracker rates could change if the BoE rate changes A LOT. I suppose it also depends on how honourable you think your lender will be - remember, they're not out to help you, they are out to make money for their shareholders (which could be you if it's a Building Society).
You need to consider the term of the deal and the fee for the deal to see what is good value.
If you or your daughter are good with Excel, make a spreadsheet that shows how much you pay each month over a 25 year term (which is typical) for a variety of products available, and you will see which offer better value. The fee is usually added to the initial loan cost (obviously, you could pay the fee up front, but you could conversely take a lower loan by having a larger deposit, so it's the same really). Put the rate in a separate column, because it will change after 2, 3, 5 or 10 years.
Personally, I like Nationwide's products, and they have online calculators that will show you what your monthly payments will be for a variety of loan scenarios. This is useful to check your spreadsheet is working correctly.
Then you need to gamble on whether you think the Bank of England will raise the base rate. How much will they raise it by, and when? I'll just pop and get my crystal ball and tell you the answer. It's on it's way by unicorn post.
Be aware that if you have access to suplus cash you could pay small amounts off your mortgage early. There are usually penalties for paying back money early in the initial term of the loan, but you can pay back small amounts. Check each product carefully. My mortgage allows me to pay back up to 10% of the original sum borrowed each year without penalty, but I can't get the money back if I suddenly need it. It used to be that I could overpay £500 at a time, and borrow back whenever I needed to up to the total amount I had overpaid.
There are products I'm not familiar with, like guarantor mortgages and offset mortgages. Guarantor mortgages are where a homeowner guarantees the borrower will pay the money each month, if they have a bad credit rating. I'm not sure of the value to lenders, because they are lending with a WHOLE HOUSE as security! Offset mortgages are where you can use your savings to reduce the capital owed, and hence the interest due each month, but still have access to the savings.
Do you need a broker? Sometimes. If you have anything unusual, like you're self-empolyed or you're trying to buy a flat in an ex-Council block, they can be very helpful. We used a broker, and I was adamant that I wanted to go directly onto the lenders standard variable rate (because it was lower than the current tracker rate), and was told I couldn't but I did need to take out exhorbitantly price life and critical illness cover to cover the entire cost of the loan, as did my partner. I wasn't impressed, particularly as we were both in good jobs and had no dependents.
I hope that's useful to get you and your daughter started understanding the sorts of products available. It might be worth a sit down with your own bank's mortgage adviser to explain all the different product types. They will have no obligation, but will come away understanding a lot more than I have explained here.
All the best,
LouP