Razor vs Ursa plays out like this. Near maximum range for your aoe you trigger it and damage ursa. As he moves closer you trigger your ulti and the damage drain skill. Then you keep out of range and hit behind you (assuming ursa doesn't have blink/lothar yet). Razor has a speed boost, which means Ursa won't ever get to hit him. After a while of ulti - armor and dmg draining him you can turn around and just kill him or keep kiting him. If Ursa gets lothar or dagger you have to get Ghost Scepter to survive him long enough to put distance between you.
Razor isn't a hero that is good against Ursa, you basically need an item advantage.
As for Razor items, it depends on the level of opposition. If you face opponents that gank you and try to deny your farm then you have to pick items that are cheap but useful. Things like Vanguard and Hood (if many casters) are great after treads or phase boots. BoT isn't something you pick on a physical DPS hero early game unless you plan on farming all game (it is too expensive). Ideal items and the way there are both a part of a build and standard for Razor is a few stat boosters and/or magic wand -> treads -> vanguard -> hood. After that you can do a variety of things depending on opponent heroes, you can even start switching around earlier if you have a team strat that requires a certain item.
I see Razor as a debuffing tank with decent DPS early game. He then turns into a semi carry late game, getting eaten alive by real carries with similar farm. Razor is basically a middle of the road hero, useful all game long, but never the best hero at anything. Kind of like Mirana, yet she has her arrow and leap compared to a static speed boost and damage drain/gain. (Mirana also has worse stats, though I think she has longer range? Edit, yep 600 vs 475.)
