Decent for a start, but if you want to go for the best times you should be aiming for under 2 hours at least, this obviously means that you should know the route decently and have an idea of what happens where and what else could happen there (RE3 has a lot of lovely randomisation). I'm not a fan of New Game+ runs myself though, I prefer fresh out-of-the-box based runs as there's more of a challenge.
The only forced encounters in this game are:
Clock Tower Nemesis
Grave Digger
Nemesis (Treatment Room)
Final Nemesis
Three of these four bosses can be killed much easier using gameplay gimmicks (lamp posts, acid, Paracelsus' Sword/Rail Cannon), so the only trouble you could have is against Clock Tower Nemesis. Who's suprisingly easy.
Take the Flame Rounds from Carlos when you bring all three components to the cable car, choose to dive out of the window (important!) at the live event afterwards, this will give Nemesis his Rocket Launcher for the showdown but it actually makes things easier. Then when you proceed Carlos will give you Freeze Rounds in the third Clock Tower room, if you take the other path he won't do this.
Load the Grenade Launcher with Flame Rounds first, it takes 6 Flame Rounds and then 5 Freeze Rounds to kill him, you can just stand in place and heal if a Rocket hits you. It's better since if he doesn't have his rocket he'll be in his tentacle form which is much worse. Besides that it's just learning enemy placements and such, you should know that pretty much every room has two different enemy layouts that can occur, none are connected. You'll learn these as you keep playing. Each puzzle has 4 different possible outcomes each except for the music and painting puzzles at the clock tower where the odds are mostly against you.
I think one of the important things to note is which weapon you get at the RPD, in the locker there is a 50/50 chance of getting either the Magnum or the Grenade Launcher, the Magnum is highly useless in a speedun and you want the Launcher. If you don't get it it'll add unnecessary time at the sub station later on.
Finally, why is there no ranking on your screencap? =P