Jeff Wills

There are a number of "basic bike maintenance" classes around. Most are in downtown-ish Portland, but I'm sure there's something near you.

Machka 

Regarding removing the grease ... if normal everyday generic baby wipes don't work ... soap does work. Pop your leg up next to the sink, squirt a bit of hand soap on your leg or rub a bar of soap on the spot. Rub a bit ... you might use a scrub brush. Rinse off the soap and dry with a somewhat rough paper towel.

CompleteStreets

It might be possible to add a chainguard to your bike. Someone may have already mentioned this, but SKS makes a chainguard called Chainboard. There's a lot of variation among different bikes, so the SKS Chainboard will fit some bikes having three front chain rings, but it won't be compatible with others. If you click on the link you'll find lots of great reviews describing the issues. Even the ones it works for run the risk of the chainguard shifting slightly over time, resulting in a somewhat noisy and annoying rubbing of the chain against the chainguard. Below is the SKS Chainboard. On this bike, the front three sprockets were replaced with a two-ring setup for the sole purpose of accommodating the chainguard. In my experience, 8 out of 10 bike shops are either unaware of such chainguards, or they know how difficult they are to install, so they advise against them.



Amazingly, some department store bikes with three chain rings come with a chainguard. I'm always baffled as to why a Walmart or Target would go out of their way to add a chainguard when major bike manufacturers still haven't found a way to do this. See below for department store examples.



Finally, I've got a photo of a one-of-a-kind chainguard made to fit a particular bike. It barely fit and sometimes the pedal rubs against the chainguard, or the chain hits the chainguard. When it's positioned perfectly it's great. It was made by someone who works with steel for a living. He made a cardboard cutout and then machined it at a factory.

CompleteStreets

If you're open to buying another bike, many IGH (internal gear hub) bikes come with chainguards. They only have one chainring in the front. The rear gears are enclosed in a cylindrical shaped hub, like below:



The downside to IGH bikes is that they tend to be 5 to 10 pounds heavier than derailleur bikes and they aren't quite as effective for pedaling up steep hills.

Rowan

By the way, what sort of chainset is on the bike? It may be that you can fit a plastic outer chainring guard that, oddly, comes on cheaper bikes. I have one fitted to an LX level chainset, and it works delightfully. I also used a double crankset on my fixed gear, and nipped the teeth off the larger, outer ring, and filed it smooth, so it became an inbuilt cuff guard.

Leebo

Wear shorts? Or tights, both work for me. Pant clip or velcro strap work as well.

Bug Shield

GoJo is a brand name but "waterless hand cleaner" will remove petroleum based grease/oil quite effectively. The key to using the stuff is in the nomenclature - waterless. Do all the scrubbing without water, then use water to rinse it off.

Different chain lubricants are more/less messy. Wax based lubes clean up easier but I don't think they suite a wet environment.

The key as others have mentioned is, don't bump the chain.

VegasTriker

Technically a chainguard protects the entire length of the chain while a bashguard only protects the largest chainring. The likely reason you find a bashguard included with cheap bikes sold by mass merchandisers is avoiding lawsuits. It is one less reason to get sued if Johnny gashes his leg on a chainring. You can find bashguards sold on eBay, Amazon and at most large online bike shops. You need to know how many teeth are on the large chainring and what the distance between the bolts that hold the chainrings on (usually 130 mm for road bikes and 104 mm for many others). There is even a You Tube video on how to install a bashguard in case you are baffled. They cost as little as a few dollars for a plastic one to well over $50 for some branded versions. Take a look at eBay to see what I mean. Type "bike bashguard and chainguard" in the search box.

Garfield Cat

If you have never done a cleaning of the chain and have no interest in getting even more messy, then let a local bike shop clean it and then have them reapply with lube that works in your area. Make sure you tell the mechanic that you want that chain cleaned very well first.

And tell him why. Let him know that its very upsetting to you that the dirty lube ends up on your clothing and skin. Guys are dirty, and ladies are not.

Chain cleaning is another skill thing.

GravelMN

I've never broken an Alivio guard. I had one on my commuter for 1,000s of miles and my extended family still has them on three of their bikes. If one does break, you have four small screws to remove to replace it (Shimano part # Y-1M2 98160). The replacement guard isn't listed on the current Shimano website, but is still available through a dealer if they are willing to look for it.


The alternative would be to ride it with the plastic guard and if it breaks, replace it with one of the aluminum guards you describe. I looked on line and many of the aluminum guards run in the $29 and up range, nearly the cost of an entire Alivio crankset. Some require that you replace the outside chainring with the bashguard, effectively turning the bike into a low geared double. I found one in the $14 range but it required a separate spacer to keep your third chain ring and looked like it was stamped or cut out of a flat sheet of aluminum, functional but not good looking.

elcruxio

Vegetable oil works. However the best stuff I've ever used so far is basic cream or base cream (same thing, whatever you want to call it). Just you know the basic white lotion stuff chicks rub themselves down with before going to bed. I get a pharmacy variety which isn't too oily and can be used instead of soap for showering (yeah, didn't know it was possible to get clean with lotion but apparently it's good for people with dry skin)
You need to use a lot of the stuff and rub a lot but it does get chain oil off from legs, hands and even under the fingernails. You do need to wash it off with soap afterwards however.

My hands have never been happier. Back in the day when I used dishwashing stuff, soap, bearing grease, gasoline or brake cleaner my hands tended to be a bit on the dry side, but now they are nice and moisturized. Feels much better than before.

Don't stress about chain tattoos. They are really easy to clean away and worrying about them might put you off from your bike which is always a bad thing.

CompleteStreets

Some department store bikes, like the two I posted photos of above, do have chainguards that protect the entire length of the chain. This is what the OP is looking for. The question remains. Why do department stores sell some bikes with these, but bike shops almost never do?