New vs Secondhand: it doesn't matter which way you cut it, when you get a new car, you pay the depreciation that new cars attract. Dealers and finance houses will wrap it up in "low, low monthly payments" to try and hide the fact. If you can do the sums to say you can afford a new car, then fine, but don't get fooled into thinking it's affordable. Look at Total Cost of Ownership over the finance period.
In terms of the warranty piece of mind, let's take some simple figures: car is £20k new; used version is £5k. Now imagine how long you could keep that old car running with £15k - you could probably replace the engine and gearbox about 4 times over if needed.
If you want to balance cost and piece of mind, look at cars 2-3 years old - a lot of depreciation has occurred, not going to be too knackered and could have anywhere from 1 to 5 years warranty left. Even if not, warranties can be bought for a couple of hundred quid a year - it's just another insurance policy.
The main reasons to buy new are the chance to pick you exact colour and specification, not having someone else's arse print on the seat, and/or major want of a brand new model; if you can live with someone else's choice of leather or cloth interior, sat nav or no sat nav, my advice is to get something a couple of years old.
Lease vs PCP vs Loan: Leasing is often the cheapest way to get a new car, but the least flexible - no easy get out clause, no option to buy if you want to keep it (although you might be able to wangle a deal at the end); PCP allows you to get out easily after half the value has been repaid, but you need to be saving up a good chunk if you want to buy it at the end (or take out a personal loan).
A bank loan is likely to be the cheapest form of borrowing - compare APRs against the PCP deals; like for like the monthly payments will be higher because there's no balloon payment at the end, but it's managed more consistently (no deposit, no balloon payment, not acceptance fees, admin fees, option to purchase fees etc.).
Personally I can't stomach the depreciation of a brand new car. There are plenty of new cars I covet, but when I see e.g. £16,000 disappearing in two years with nothing left to show, it puts things into to the perspective of my income.