No, you don't have to book the survey when you get the memo of sale. You book it when you feel comfortable that the process is going as expected.
Depending on your deposit size, your mortgage lender might want to see the house in person before they'll agree to lend you the full amount. We're about to go 90% LTV so our lender has just visited the house. We're awaiting confirmation from them that the house is worth what we've offered for it. If their view of its value versus what we've offered differs by more than 5k, we simply can't make up the difference, so I'm not prepared to spend money on a survey until the first hurdle is passed: the bank will lend us the full amount. Of course we could always go back to the vendor and negotiate, but there's no guarantee that would be successful. I've also got my solicitor on hold until the mortgage is approved too - they tell me this is really, really common. They haven't even ordered searches yet - because as soon as they do you start passing over money in £250-300 chunks.
From someone with not a huge amount of savings for post-move, one of my priorities is absolutely not spending money until I'm confident it is the right step in the process to do so.
Everyone else on mumsnet will tell you to full on in - order the survey, start the searches. But, for the most part, they aren't FTBs and don't remember how scary and expensive it is first time round!
The mortgage lenders 'valuation' is free, by the way - and they won't necessarily tell you how much THEY think the house is worth, they'll just approve the mortgage. Same in-person check happened with a different lender on a different house when we were at 95% LTV. Our broker tells us it's common for higher than 80% LTV. For those with larger deposits, the lender usually just does a desktop or drive by valuation (drive by meaning: I saw the house with my own eyes and can confirm it does actually exist!).
If you're in the same situation, you can call the surveyor and ask them to book a slot in, say, 3 weeks time. This should reassure the seller that you're serious, and surveyors don't usually want immediate payment, it can happen a day or two before the appointment. So if your bank valuation comes short you haven't forked out any money yet.
Level 3 is recommended for: houses over 90 years old, those with extensions, or significant internal alterations, e.g. walls have been knocked down and moved around.
We're about to pay £725 for a L3 in the North East. Adding getting it valued onto that would be an extra £50.
You can feel free to ask them for a sample report of a similar property type. I've swerved the one who say 'we can't do that because they're all so very different.' The one who sent me a sample report without me even asking is getting my business.
Another difference between L2 and 3 - and any readers, please correct me if I am wrong - is that with a L3 they will also cost up any works they think need doing, which work on a traffic light system: red - hardcore danger, needs immediately resolving, amber, will need attention in the future, green - checked and all good.
They won't check the quality of any electrical installations or pipework. You may get general comments such is 'consumer unit appears to be quite new' or 'pipework may be lead.' They will comment on the strikingly obvious, e.g. 'gutter from roof to kitchen has a large crack.'
NB, anything they are unsure about, they're gonna tell you to get a specialist in to check. That's their arse covering. You'll get that on any survey - but - you can pick up the phone to a surveyor and off the record they'll usually be quite friendly and give you a sense of whether a problem looks like a really big 'swerve this house' or not.
You can ask to buy the previous survey off the previous buyers, but usually when that happens, you lose any power to sue the surveyor for missing glaringly obvious, expensive things - they have liability insurance for missing things, it's part and parcel of their job. But, generally, if YOU did not commission the survey, you have no recourse for it being wrong. A PP mentioned some are shareable - I don't know about that. I know mine says 'do not share without permission.'