Like any plant, in the right conditions and with an appropriate care routine Phragmipediums should be easy. Personally, I find them to be one of the easiest orchids to grow and bloom indoors, but obviously, not everybody shares that sentiment. It's hard to say for sure if you'll find them to be as easy.
Most Phrags are water loving plants, and if grown appropriately, it's practically impossible to over water a healthy plant. In fact, the biggest concern with growing most Phrags is making sure they do not dry out. There are caveats to this, but I'm not going to delve into that. For the most part, I water frequently (every 1 - 3 days) and leave water in their saucers at all times. Water quality is also more important for Phrags than for many other types of orchids. If your tap water is hard, contains lots of salts/minerals, and is full of cholorine/chloramine and chemicals, you'll find Phrags do much better if you incorporate some rain water, reverse osmosis, or other pure water sources into your watering routine. You may also need to flush the pots with lots of water periodically (once a month or so) to remove excess nutrients and keep them from building up.
Phrags are medium light house plants. There are some species and hybrids that do well in shadier conditions (bright Phal light), a few that prefer higher Cattleya level light, but most are going to grown and bloom well in bright light protected from direct sun. For the most part, you're aiming for light green leaves, rather than dark green leaves.
Temperatures should be intermediate, and generally I'd say typical indoor temperatures work great. As mentioned, most Phrags and especially most hybrids aren't going to need temperature drops or anything special in this regard.
Another thing to consider is that Phragmipedium flowers aren't long lasting. Each flower tends to only last 10 - 20 days. They are sequential bloomers mostly, holding 1 - 3 flowers open at a time (more if the spike is branched). Flower don't wilt or fade before they drop off, so when they do drop, the look perfectly happy and healthy. Also, as mentioned, some Phrags produce branched spikes.
Phrags, especially the hybrids, are fast growing compared to many other orchids and they will often bloom multiple times a year if you give them good growing conditions year round.
For a beginner, I mostly recommend going with hybrids, though many Phrag species are just as vigorous and easy to bloom. As for small growing hybrids, look for crosses that involve species such as P. pearcei, P. caricinum, P. klotzschianum, and P. fischeri. If you like red/orange colors, you'll want to search for P. besseae and P. dalessandroi hybrids. If you like pinks and purples, go for hybrids with P. schlimii (note: this species is fragrant and can pass its rosey fragrance on to some hybrids) and especially P. fischeri (it's a tiny grower). If you like greenies, stay away from hybrids with besseae, schlimii, and their relatives. There are some nice small growing long petaled hybrids. Though these can sometimes be a little trickier to grow and bloom, there are crosses with P. humboldtii and P. warszewiczianum (formerly wallisii) that would be good to consider especially if they involve other small growing species. Finally, the big flowered Phrag. kovachii actually isn't a terribly large growing species, so if you see a cross with this species, you don't necessarily have to rule it out. Like the long petaled hybrids, I would say it's probably better to get a little growing experience under your belt first, but it's not absolutely necessary.
As for information sources regarding parentage:
OrchidRoots is a good source, you can search by species to find hybrids, search hybrids to find parentage.
Slipperiana - Main Page. has a lot of good photos and for each species a list of hybrids.
I recommend looking up trusted vendors and seeing what Phrags they have, getting an idea of what your preference is, then looking those hybrids up to double check parentage and get a better idea if they are small growing.