forget laser - good for office work ie reports and documents - crap for photography
Inkjet is the only type. You need to pick between short or long longevity of the print first before deciding on what printer model:
Short term - dye based inks
Less than 10 years in an album (5 years on a wall inside out of direct sun light)
Has the best colour reproduction available.
Long term - pigment based inks
Accelerated tested to give 70 to 100 years in an album (estimated at 30 years on a wall out of direct sunlight).
Not as good as ink based but can be equal or better than commercial "mini lab" type prints you would normally get from K-Mart, Hardly Normal, etc.
Once you know how long you want the print to last, then pick the suitable Epson printer to give you this. Epson are the best I have ever found - far surpass HP and Canon for print quality.
Something you should also look into is the ease of getting replacement cartridges - you cant generally purchase high end printer inks from outlets like officeworks, dick smiths etc.
I use an Epson R1900 which comes with pigment based inks but I also have an aftermarket ink tank kit which runs dye based inks. The pigments are worth about $25 per tank and it has 8 tanks. The gloss cartridge goes pretty quick. At least you dont have to replace all the colours in one go (single colour tank).