You normally want to use outdoor flooded cable (also called gel-filled) as it is designed to weather the elements. I have a few clients who have gone with outdoor flooded & shielded cable as they were worried about interference on the outdoor runs. Also look for UV-resistant cable if it's not going to be buried or otherwise enclosed.
As for Cat 5e versus Cat 6, for home use it probably won't matter as you most likely running 100/1000B-T Ethernet and it will run fine on both Cat 5e or Cat 6. If you want to try to future-proof your cable--or the price difference is negligible--you can go for Cat 6.
If you want to bury the cable directly in the ground then you need to use direct burial-grade cable and not "standard" cable, otherwise you need to use conduit.
First you need to consider the distance to the poll. Depending on the distance and use of the cable, you might be able to use RG6, but you also might need to use RG11.
You want to bury it deep enough that you won't cut it with a shovel should you do any yard work. They are usually a couple feet deep, but it depends on climate and location.
Make sure to call your utility company (usually your gas company) and have them come out and mark all burried cables/gas lines BEFORE you start digging - the last thing you want is to break a gas line or an electrical feed (ZAP!).
Leave yourself plenty of slack (service loops) at both ends of the cable. Overtime the ends will get cut and replaced over and over, and you need some extra cable allow for this.
You might want to check to see if your cable provider will even allow this, often they handle the last-mile connection to your demark. Because cable is "shared", a crummy installation on your end can cause issues for other customers.
Best Answer
After a quick google search, I've estimated the dimensions of the cables as follows:
So to run just these two cables, you're going to need 3/4" conduit (based on NEC Chapter 9 Tables). If you run two of each cable (4 total cables), you'll need 1" conduit. Three of each (6 total cables), you'll need 1 1/4" conduit.