If you're interested in thoughts from someone who has played TF in ranked around the ELO you are looking to play at (54% win rate through around 50 games in bronze/silver with over a 3 KDA - not great but not terrible), below are mine.
In my experience, gold card is almost always better than red card. Although it sounds great in theory to be able to do AoE damage with red card, you don't ever want to hold the card to try to wait for enemies to bunch up, as you are losing DPS while waiting.
Further, in my experience, in low ELO games a stun is ALWAYS huge in team fights. The stun can be used defensively as peel if someone is coming at your or your ADC you can stun them. Additionally, stunning someone will usually mark them as a target allowing your team to focus its damage on that target. In low ELO, where coordination is hard to come by, this is huge.
Additionally, stunning someone allows you to guarantee that you will hit your q on them. This is a TON of damage, and a gold/q/aa sequence will kill almost any non-tank after mid or late game. Although his kit has AoE elements to it, and he has great AoE poke, TF actually has amazing single target damage because of lich bane, his W, and his E.
In my opinion, TF is valuable in solo queue because he is very flexible and offers a lot in a lot of different situations.
Obviously, this starts with his ult, which lets him easily gank sidelanes to get your bot/top rolling. Bot laners tend to be very worried about a TF gank, but top laners frequently seem to push up in bronze/silver setting themself up for a gank.
His stun works great for picks, and his ult can even be used to help catch someone out (both by providing vision of a caught out enemy and teleporting to cut off an escape with a gold card).
His q offers both great poke and great wave clear, which is good for both offensive and defensive sieging. Further, he does very solid damage against towers, which is rare among AP champions.
His only real drawback is that in most matchups against common champions you see played in bronze/silver you will need to be better than your lane opponent to apply pressure. TF actually has a really solid laning phase thanks to the range of his q and the mana sustain of his w, but applying kill pressure will require getting up into your opponent's face, which can be very risky, especially against any opponent with CC. That being said, he is the king of ganking side lanes, so it's not that big of a deal.
All of this being said, I believe that trying to climb primarily using any immobile mage (other than Syndra) is more difficult than using a more mobile character that can burst and snowball.