You already have lots of great advice here.
Pros--flexibility! You can go to any small village, take any side road, stop at any mildly interesting site, choose your pace, and choose your food. The joy of discovery and the fun of figuring it out if you like that sort of thing. But mostly the flexibility and pace. See the movie Paris Can Wait for inspiration
Cons--You're on your own. People are generally helpful, though. Also, possible lines at attractions. And you might miss something or not have all the information you want. But of course the discovery is more important for some than knowing every detail about a place
Fully guided tours:
Pros--no hassle or thinking about where you are staying or how you get from point A to point B, which is a huge relief for many people. Also, you can meet lots of wonderful people. Generally great for bypassing attraction lines, making sure you hit the highlights
Cons--Want more time here? Sorry, the tour bus is leaving. Tend to stick to bigger sites
Pros--You can customise your experience and get a local to make sure you hit the things you want and to answer all your annoying and weird questions, often great recommendations and even reservations for food, most of the pros of the guided tour depending on level of customisation
Cons--Cost, somewhat isolated from other travellers
Pros--get help navigating that attraction with the long lines or a trip to the place where language is perhaps more of a barrier, meet new people, lots of information
Cons--Less joy of discovery, sometimes limited flexibility
I would say if you are moderately adventurous and of the mindset that glitches in your plans make great stories, go more DIY and throw in the odd day tours. If you are of the mindset that you want it to be hassle free, easy, and don't want to think but just drink it all in, private or package tours are your best bet. Group travel has led to many a special friendship, with people booking trips together for many years, but intimate experiences with a close loved one are also very special. More nervous? Book a tour. Think getting stranded on a rural road and using lots of gestures to communicate in a village sounds like a great story? DIY. Want to make sure you get all the important sites and information without spending time in long lines? Book a tour. Want to stop at that quaint cafe full of locals for a spontaneous beer or lunch? DIY.
Note that tours may sound expensive, but you do get a lot for your money. When you do the math of things like hotels, meals, town-to-town transport, and attractions, you are often paying similar prices to what most people spend on their DIYs. Unless you are particularly savvy or the hardcore backpacker types, you won't save all that much on a DIY. We've done bus tours (with students--we are teachers), and we've found them to be super fun. But when not with students we prefer DIY. One of our favourite stories is finding a dog on a highway in Catalunya and trying to communicate that we were looking for the owners in the nearby village (she was returned home safely). We never would have stopped at that village otherwise, but it was beautiful, and we had some interesting local interactions.
There is no right or wrong. You know your own comfort level, interests, and hopes for this trip. Lots of first timers prefer the security of tours, where your guide will help if you lose your passport or need translations or food recommendations.