Hi that's very exciting.
I would go onto rightmove or zoopla sold house prices and see what properties have gone for in the past - you'll get a better idea of what it is worth. Have a look on what is currently on the market too.
Have a look round a home and check anything you are particularly bothered by (I weirdly always ask to turn on the showers as I had pathetic showers and putting in power showers can be expensive) - see if there's any damage to the property - mould, large cracks, uneven floors etc.
Put in an offer you think is worth it and what you'd be willing to pay - make sure you take into account legal fees, stamp duty, mortgage fees, surveys and redecoration fees and any other repairs it would need.
If it is accepted great, if not there may be room to negotiate.
Appoint a conveyancing solicitor (also check with your mortgage company if it has to be someone approved by them). Also go back to your mortgage company with the agreed price and check they will stick to the full amount they offered (this isn't always the case), they will also send out a surveyor of their own to check it's worth what they're paying. if you're putting down a very small deposit the result of this may affect what they're willing to give.
Appoint a surveyor who will look round the house and see if there's any major issues - do not skimp on the surveyor. There's always gonna be a few issues with any house but a surveyor should point out any big flaws. if it's something big that's gonna cost a lot to fix you can either just get on with it, try to renegotiate a price or walk away.
Then just wait...and wait and wait. Conyenencing solicitors are notoriously slow. Eventually you'll get to exchange which is everyone signing the contract saying you'll move on a particular date and pay this price. You are now responsible for the house even if you aren't living in it so make sure you get some insurance.
Completion day is moving day - I'd recommend a completion at least two weeks after exchange to sort packing and movers etc bear in mind as well things like sofas and beds can take months to order so make sure you've got something in the meantime.
Move and celebrate (cheaply as you will have no money)
As for lease v freehold. If you're buying a flat it will be hard pressed to find a freehold but i wouldn't buy a house on leasehold. If you do leasehold make sure you check the fees etc carefully and the lease should be well over 100 years at time of purchase.
Avoid new builds like the plague - every one i know whose bought them has regretted it, usually ending up with loads of issues inc damp and the resale v purchase value is redic low and intial purchase price is way more expensive. they're not great investments.