Buy a slow cooker.
They're cheap, and it will cook your food slowly in around 6 hours.
Don't overcomplicate things: http://en.wikipedia.org/wiki/Slow_cooker
cooking.stackexchange.com/users/968/codeinthehole
Cooking in a water bath in vacuum sealed bags is called sous vide .
The advantages include: all of the meat is cooked to the desired temperature, and no higher, so you get 'perfect' doneness.
The fibres of he meat don't contract due to the high temperatures and squeeze out the moisture, so the meat stays very tender if you have the right setup, you can put it on an leave
it you can include flavourings in the vacuum bag
so your meat steeps in the flavouring whilst it cooks.
Disadvantages include: it can be expensive to set up (though not always , as work arounds exist)
it can be difficult to keep at a constant temperature if you don't have an expensive set up
the meat does not have any outer crust (although this is easily remedied after the cooking) takes a lot longer to cook.
I think it will be difficult to do in an oven as it is not often that ovens go as low as this type of cooking requires.
cooking.stackexchange.com/users/210/Sam Holder
If you want low temp, you should go with braising.
The low temp and moisture work wonders on meat with lots of connective tissue.
Plus, no expensive tools are required.
The downside is it takes TIME...
possibly measured in hours.
You cannot cheat a braise from what I've seen or you'll still end up with tough meat full of connective tissue and not deliciously broken down tissue.
Cheap tools of the trade are aluminum foil and a cast iron dutch oven.
Sear the meat first to get some good browning.
Toss in the foil and make a pouch and put in some marinade.
Seal up tight.
Toss in the dutch oven and then into the real oven.
Sous vide looks great on TV, but most people have what they need to braise sitting in their kitchen at this very moment.
Especially if you have a little something called a Crock-Pot.
An aside: Crock-Pots are a great alternative to an unreliable oven that probably wastes lots of energy.
cooking.stackexchange.com/users/788/VoutilaD
Here's the best link on sous vide at home
I know: http://www.seriouseats.com/2010/04/cook-your-meat-in-a-beer-cooler-the-worlds-best-sous-vide-hack.html
For meat, you can do small cuts for short periods (hours) at low temperatures (under 150) in a beer cooler.
I've done this and it works pretty well.
cooking.stackexchange.com/users/986/Dennis
For a few of your questions, a query of your favorite search engine will suffice; however, a skimmed version follows: timings and weights advantages of low heat
yes:
it all depends really on the cut of meat, and your ultimate goal.
Some might not agree with me, but you need to sear the meat.
either before or after the cooking.
some sear it on high heat for 3 to 4 minutes on each side and then put the meat in the oven; others cook the meat and sear it at the end.
it's your choice!
season it with salt and pepper.
be generous with the salt.
buy an oven thermometer, they're like $4 and adjust your oven accordingly
cooking.stackexchange.com/users/87/dassouki
I want to try out low temperature cooking of some meat, e.g. beef  I don't have a reliable oven and am looking for advice before starting. Or alternatives to ovens.  I heard some people use meat in vacuum sealed plastic bags that they cook in a pot of water, (easier to measure temperature?)  What are the timings for weight/temperature combinations?  What dis/advantages does low temperature cooking have compared to grilled?  Anything else I should now before trying out?
Advice for low temperature cooking
cooking.stackexchange.com
<meat><slow-cooking><sous-vide>
cooking.stackexchange.com/questions/1959
cooking.stackexchange.com/users/876/HeDinges
An oven will usually not go low enough to cook this kind of way, but you could use a slow cooker or aluminium foil with a cast iron dutch oven. A slow cooker or a dutch oven would be useful and inexpensive ways of trying out slow cooking.
Try a slow cooker. It is difficult to do this in a normal oven as the temperature often doesn't go low enough. Try using a dutch oven for slow cooking in an oven.