I am looking at homes to buy and I want a fireplace. I am not familiar with a gas log fireplace but fairly familiar with a wood burning fireplace. What is the difference between the two different fireplaces? Also, what are the advantages and disadvantages between the two? I don't have tons of money to pay on gas logs. Are they expensive? How do they work?

Thanks in advance for anything you can share with me about fireplaces and helping me make a very important and potentially costly decision.

I am going to give you as complete of an answer as possible since it sounds like installation cost, cost for fuel use, looks, and heat generation are all issues you want addressed.

Vented Gas Logs: These are essentially the cheapest and worst of the gas log variety. Their origin is from the 70's and they tend to be inefficient and expensive to run. Essentially they are a wood burning fireplace complete with chimney and have a burner that sits under a rack with ceramic logs. They are very low maintenance and do not need regular chimney cleaning but a chimney inspection every few years is advisable.

The worst thing about them is most building codes dictate that the damper has to be blocked open or disabled 24/7 on a vented gas log, so they do not accidentally back-up poisonous fumes into the house. This feature alone makes them ridiculously inefficient. You can use a Chimney Balloon in the flue when you are not using the gas log to stop the cold air from rushing down the chimney into your home.

To make matters worse they are inefficient at generating heat (sending most of it up the flue) and if you don’t have glass doors it will also suck in and waste your already heated interior air that your poor furnace had to work hard to heat. I don’t sell these in my shop & I don’t recommend them.
Cost for install = $500-$800
Fuel and heat efficiency = 1 star (terrible)
Looks = 4 stars (nice flickery flame)

Vent Free Gas Logs: These are units very similar to the other style in looks, but with some very important changes. Vent free gas logs do not need a chimney (or shouldn’t anyway) and they put all the heat they produce into the room.

Unfortunately, they also put all the fumes they produce into the room so they do effect your indoor air quality. It is kind of funny that the manufacturers of these units say "oh, the vent free units just put a little moisture into your homes air and a teeny weenie bit of fumes." then in the next breath they say "Vent free gas logs are not designed to be a home heating device and they should be used in a ventilated area". Bottom line is...if you burn a fossil fuel you get fumes that are bad for you and it is not healthy to put those straight into your living area. Bottom line is they are good at creating heat and ambiance but bad for your indoor air quality.
Cost for install = $500-$800
Fuel and heat efficiency = 4 star (good, but with dangers)
Looks = 4 stars (nice flickery flame)

Wood Burning Fireplace: It sounds like you are already familiar with these. They are inefficient at generating heat since they tend to draw in more heated interior air than they return to the room. Most open wood fireplaces have dampers but they can be leaky even when closed and used properly so a chimney balloon is an alternative to use as an efficient damper. The chimney needs periodic cleaning and inspection.

They can be converted into gas log fireplaces if you have propane or natural gas service that can be run to the hearth.
Cost for install = usually built with the house but can cost $2K-$10K to add onto an existing home.
Fuel and heat efficiency = 1 star (terrible)
Looks = 5 stars (nice flickery flame)

*Note* You can of course add glass doors, outside air ports, heat exchangers/blowers to any of the above units, and these will help the efficiency in some cases. However, they are by design inefficient units.

Gas Direct Vent Fireplace: These are closed combustion units. You cannot open the glass and get to the fake logs. They are very efficient at generating heat, but do not look very realistic. these can be used to heat a home or at least a zone of the home. They do not have a chimney but rather vent directly through the wall with small PVC pipes.
Cost for install = $1000-$2000
Fuel and heat efficiency = 4 stars (quite good at 70% efficiency or better)
Looks = 2 stars (stove like blue flame, not flickery)

I have a regular fireplace without a flue or anything...and natural gas logs. I would like to have a gas ventless fireplace. Do I just buy ventless logs, a remote and seal off my chimney? Would it be better to do a direct vent? I'm trying to keep my fireplace..I would like to have doors (which I believe I can close the doors for a direct vent) but not have all my heat go out the chimney, which it currently does.

We had an existing gas line in an existing fireplace. We did a direct vent which was REALLY easy. They just put the vent "pipes" in your existing chimney and attach it to the gas fireplace insert. If you get it with a blower, it will blow the hot air into the room. Most of these gas inserts are so efficient they can be considered a heat source for a home.

Ventless fireplaces are not good if anyone in your home has asthma. Also not good for pets, especially birds. Also not good in small rooms. Also ventless can cause moisture problems. It is usually recommended that you have a carbomonoxide detector if you run a ventless fireplace in your home.

Hope this helps a little.