FTB with cash

You don't need a solicitor immediately, but try to get one soon; preferably local and recommended by someone you trust. Solicitors will be able to give you a breakdown of their standard fees, though some purchases may require extra work.

Unless you're in Scotland, a solicitor will probably not be fully conversant with local house prices. It's your job to explore the sold price history of comparable houses on Rightmove to see what properties like those you're considering actually sell for.
Ignore Zoopla's averages, which may not be very accurate.

View the houses without assuming you'll make an offer on any of them right away. It takes time to mull over the pros and cons of a property, so I'd not offer until after a second or third viewing, unless the market in your location is 'hot.' Even then, with so little experience, making a snap decision would be risky. You'll only be a FTB once, so don't waste it.

Once you know what houses of that type usually sell for, you'll be in a better position to know what to offer. Typically, people don't offer asking price immediately and there may be some horse trading before a price is agreed. You don't need a solicitor to make an offer for you in England and Wales; you can do it by phone or in person through the agent. A few of them may try to mess with your mind when doing this, but stick to your guns whatever the reaction - after all, you've researched prices.

Always remember that the agent works for themselves first, the seller second and you, the buyer, have no contract with them at all. They may ask you to prove finances, but don't reveal how much money you have altogether; your solicitor can confirm you have the means to pay, if necessary.

Even after you've had an offer accepted, don't assume that's it; you can still pull out until exchange of contracts in E&W. Many of us have done this after discovering something, either in a survey, or simply by playing detective in relation to the house. For example, you might find out the house is in a high flood risk area, or after staking it out at night, you might notice rowdy youths congregate in the bus shelter close by etc etc. You might even find a better house.

If you have an offer accepted, the owner may want to see some sign of commitment from you before removing the property from Rightmove/Zoopla/whatever. You, on the other hand, may want to see SSTC on the ad. Negotiate. Booking a survey is a way to show you are serious. Types of survey vary according to age/type of house. After a survey you may need to re-visit the price, or even walk away if something really bad is found.

What else should you be doing? Reading the stickies at the top of this forum and a host of stuff on the internet. It's all out there.....more than there ever has been. Good luck.