This is a guide for Shen. It actually resemble my gameplay style, as i am playing solo. I will explain my choices in the next chapters.

As you solo with Shen, you want to harass the enemies, to sustain yourself in lane and survive ganks.
Greater Mark of Health - The bonus health from these runes will maximize the potential of Vorpal Blade and Ki Strike, as you can do a little bit more damage and sustain a little bit more through Vorpal Blade.
Greater Seal of Armor - The bonus armor from these runes will give you the survivability that you need in lane.
Greater Glyph of Magic Resist - along with Greater Seal of Armor will help you survive in lane.
Greater Quintessence of Health - along with Greater Mark of Health will help you sustain yourself in the lane and harass more.

You are playing tank/support Shen so you need to be able to help your team in every way you can. Choosing Heal, will not just help your team in team-fights but will also help you survive ganks or sustain yourself in lane as you solo.
Soling, in my opinion, is best suited for Shen. Taking Exhaust will help you taunt the enemy at your turret and keep him in turret range as he takes damage.
For a more aggressive play you can choose Flash as a positioning/escaping tool and Ignite for a little bit of extra damage plus the reduced healing effect.

As a tank you need the bonus armor and bonus magic resist given by Resistance and Hardiness . Also Runic Affinity will give you that extra Baron Buff time and will allow you to be even more tanky for a while.
Also as a support you need the bonus healing given by Summoner's Resolve .
As you are the initiator, you need to be able to initiate very often so Good Hands is a must.
Soling can be very difficult, and sometimes you need to go to base, for purchasing items or for recovery. You need to be back in the lane as soon as possible. The combination between Improved Recall and Swiftness allows you to do that.

Vorpal Blade, as your main sustainability/damage source must be taken at level 1 and maxed first.
Shadow Dash must be taken at level 2 in case of low level ganks, bust maxed last, as you will need it mostly in late game.
Feint, as you solo, you must take it at level 3, as it can completely cancel your enemy's harass.
Stand United is taken whenever you can (6, 11, 16)

Pros

• Extremely powerful solo
• Extremely resistant tank
• Buffing the team and debuffing the enemy

Cons

• Small damage output
• High cooldowns
• Weak pushing

Actually this is the full build, from late game.
Start with Doran's Shield
Immediately build your Ninja Tabi
Then you have to choose:
If the enemy's main output damage comes from magic damage, you should build Force of Nature and then Warmog's Armor.
Otherwise you should build Thornmail -> Force of Nature -> Warmog's Armor.
As a support you can buff your team mates with Aegis of the Legion and also debuff your enemies with Abyssal Mask. Also the AP from Abyssal Mask will buff your shields and will give you a slightly increased damage.

• Always keep a target marked by Vorpal Blade and always take advantage of the sustainability it offers.
• Don't you ever think that you are unkillable when soloing. Analyze the gameplay of your enemy. If he is aggressive, try to play a little bit defensive. If he plays defensive, harass him whenever you can and push as hard as you can.
• The combination between Vorpal Blade and Ki Strike is a very good tool for harassing the enemy.
• Taunt your enemy in your turret range and keep him there with Exhaust while you do as much damage as you can through Vorpal Blade Ki Strike combo.
• Ward whenever you can. Its your best defense against junglers or ganks.

You can face a very wide varieties of champion combinations while you solo. Keep in mind that every combination will have a strong point and a week point.

• While you solo vs a melee champion, the ownage of the lane is guaranteed. You can play aggressive, harassing him and even taking a kill or two, but be aware as you face just one champion, it means that they have a jungler as well.
• Very often I face Garen as counter solo champ. Hit him with Vorpal Blade whenever you can in order to cancel his passive. Avoid being hit by Decisive Strike using Shadow Dash and when that is on cooldown use Feint.
• While you solo vs a ranged champion, always play defensive and count on your jungler's ganks. It is the best way to avoid getting killed.
• While you are 1v2 on top, vs a ranged champion and a melee one, harass the ranged one with Vorpal Blade and the melee one with Ki Strike. Also play a little bit defensive and ask for ganks.
• The hardest solo ever is when you solo vs 2 ranged champions. In that case you will need a lot of ganks, and even if it's shameful, hug the turret and kill minions there. Also taunt one of them or even both of them when you can and let the turret do the trick.

There is a simple set of rules that you must respect:

• Always tell your teammates when you counter lane is missing
• Always look at the map to see a potential team fight or a gank. Whatch your teammates and use your ulti whenever you think you can turn the tides against your enemies
• Ward carefully. You do not want to waste your money on wards
• Don't be greedy. Use your Heal to save lives. Yes you are also a support and it is your job to do it.
• Tower dive
• Do not steal kills. You are allowed yo kill only your counter lane in ganks or whenever your team may loose a low health enemy.
• Taunt often
• Tank the turrets. Turret dive when you gank, especially in mid game. Yes, with this build you can easily tank 2 turrets and an ad carry. I've done this very often.

Play Video /league-of-legends/champion/lee-sin-73

This is not my final guide as I will continue to update it whenever I'll have more info (like vids/prints).
Also please let me know if you find any flaw in my build/english (yes english is not my mother language).