Never thought about size affecting flavor. Most of what I’ve purchased has been Robusto, I think. I was told that was an average size.
Robustos are definitely the most common size, and it's actually difficult to find a cigar that doesn't offer that as one of the sizes in the lineup.
Torpedoes are a favorite for some, and depending on the angle of your cut, you can direct the draw wherever you want to in your mouth, and perhaps get some more flavors from the stick due to that shape.
If/when you decide to move up to a "good" cutter, you'll find it to be a much nicer experience as well. The easiest way to make sure you don't cut off too much or too little is to cheat a bit. Set your cutter on a flat surface, and hold your cigar upright, putting the cap through the hole and onto the table, and then cut. It's practically foolproof. Some may look down their nose at you. I would mention that you're new to this, and if they have some tips, to offer them up. I still cut some smokes this way, and I wouldn't consider it to be a bad thing at all to start your smoke off with a good cut. You CAN wreck your cigar with a bad cut, so I wouldn't worry what someone thought of me, and I suggest you adopt the same view
I have had a multitude of cutters, and I've given away or left many that were serviceable, but not at the quality of my 2 favorite brands. Xikar and Palio are, IMO, the best cutters around. Colibri makes some decent cutters as well, and their V-cutter is outstanding. Same thing, the cut can change the experience. A punch cutter is practically foolproof, as it just cuts a little circle from the cap, but I would make sure it's sharp, otherwise it could take too much effort and cause you to split the cap. A good punch cutter is a joy to use, BUT, a punch cut can concentrate too much of the smoke or cause it to become bitter too soon. I've got a Xikar punch on my keys at all times, and I'm going to be picking up the PerfecPunch next week. I've got a Nub punch cutter that's okay, but it was a throw-in promo, and after I get the PerfecPunch, I'll be giving the Nub punch to a buddy who wants to try it.
For now, whatever you have is perfectly fine. If you choose to invest more, I recommend CigarBid or some other sale to get a Xikar or Palio. The msrp for both can be a bit of a sticker shock, but none of my Palio's were more than $15 from Cbid, and my Xikar was half the regular price since I didn't care about the color. Still a lifetime warranty and free sharpening, if needed. The Colibri V-cutter was probably my most expensive cutter, but you'll see why if you look at the limited offerings in V-cutters.
Same with lighters - a triple torch is great for what I prefer, but is completely overkill for corona's and other smaller sizes, and single torches can be had for a song. The only lighter I wouldn't recommend is a stock Zippo. The fuel may add unwanted smells or flavors. They make torch inserts for Zippos, so you can use that if you have a favorite Zippo. Thunderbird or Vector is the only insert I would trust, and I'd give the edge to the Vector inserts.