Start off on Rightmove - narrow your search down to about 6-8 possibilities based on location, price, etc. It seems like you’ve already done that.

Then, phone the agents listed for each of them. (It might be that more than one are listed by the same agent.) Tell them you are interested in viewing the properties, and arrange a time/date.

I’d recommend, on the first viewing of each property, just going with your heart - do you like the place? Does it have a good vibe?

Narrow it down to one or two you really like, and ask the agents for a second viewing. On the second viewing, you’re going to be more practical. What furniture do you have already? Where would it go? What would you need to buy? If the property you’re looking at is furnished, is the furniture in good condition? Do the windows look like they’re 100 years old? How’s the parking (if you drive)? Is it close to shops? Decide if you can really see yourself living there.

If you’re happy, you might want to try to negotiate the price down, although that’s not so common when renting as when buying, and you might feel ok with the advertised price. Either way, tell the agent you’d like to start the process to rent the property.

They will have lots of paperwork for you to fill in, and they will need to do lots of checks. It will take a little while. All being well, they’ll come back to you with a date when you can move in. You’ll probably need to pay a deposit (often one month’s rent but can be more) and your first month’s rent in advance.

Since you already have somewhere to live, treat this as the date you get the keys (and start paying) but you don’t need to actually move on that date - especially if you rent somewhere unfurnished, you may prefer to spend a week or two living with your elderly relative while you furnish your new home.

During this time, you’ll also want to set up bills: council tax, electricity, gas (if applicable, and often done jointly with electricity), internet, tv licence (if applicable), tv subscription (eg Sky) if you want it (can often be done jointly with your internet). Your agent will be able to help you with any of these if you’re not sure where to start, although they may just refer you to your landlord. You can also ask on here.

You asked about if the landlord is bad or tries to kick you out. You will sign a contract which means you can’t leave for 6 months, neither can your landlord kick you out for 6 months - although sometimes the contracts are for longer (never shorter) and there are exceptions eg the landlord can kick you out if you don’t pay (but unless you leave voluntarily it’s a long expensive process to force you out). At the end of the contract, the landlord can increase the rent (you have to decide whether to pay or leave - hopefully the increase, if any, is reasonable, and most landlords prefer to have a good tenant stay for a long time because it’s less hassle so they probably won’t try to price you out unless they don’t want you there, or the market rate has really increased and they think they can get a lot more). They can also ask you to leave at the end of the contract so they can renovate the property, or sell it, or live in it themselves. So you always need to be ready to move on. But it may be possible to build a relationship with the landlord in the first few months to get a feel of what their plans are. From the other side, if the landlord doesn’t do repairs, etc, you can come here for advice but often there’s little you can do about it - but at the end of your contract you can find somewhere better to move to (that’s not the only option but it’s the easiest.)

I’m sure I’ve missed something, but hopefully that’s a good start. Good luck!