For a turbo build, I say go with a B18B (
http://www.hmotorsonline.com/shop/sc2000search.cgi?what=page&item=30007) and keep it stock until you can afford that turbo kit. Once you have the turbo ready to install, then start the build process. Start by adding a thicker then stock head gasket to lower the CR a bit (cheap and easy way to add a little more peace of mind when running boost on a DD). You would also be good to go by mating it to a stock B18B 5spd transmission as well, given that these are geared well for boosted applications. Then follow up with the mainstays of a turbo build such as large diameter exhaust piping, free flowing intake elements boost controllers, inter-cooler, etc. I say do these things AFTER you are ready for the turbo, because parts such as large diameter exhausts aren't exactly ideal for non turbo engines.
There are a few reasons why I say this;
A) Availability. The Integra LS engine (e.g. the B18B) is a very common engine and is rather cheap as far as B series engines and transmissions go.
B) Turbo. The B18B has a lower CR (compression ratio) than any other B series engine (basically the B16A or B18C variations, & the B17 as well). Lower CRs are what you are after if you want to run boost on a daily basis, especially at a higher PSI. This will allow you to run more boost while keeping it within safe cylinder pressures (read: you won’t grenade the engine as easily). This is something important for anyone of your knowledge level trying to run a boosted Honda motor (with stock internals).
C) Cost. Again, this engine and transmission will, on the average, cost you less than the B16A or B18C motors and transmissions.
D) Ease of install. As with the other motors listed in this thread, this is a basic drop in swap.
What’s more, this motor will give you very good drivability in the meantime while waiting to get that turbo bought and installed. The B18B puts out more torque then your Civic was ever meant to see, making it a very well suited engine for daily driving. Not only will it be a good deal faster then what the car had with it's stock engine, it will "feel" quite a bit faster due to the added low end torque (rofl @ torque and an NA b series).
Now, with all that said I have to digress a bit.
You wouldn’t believe (or maybe you would) how many kids I’ve heard who say they are "going" to turbo their car "at some point". You may fully believe that you will, as I am sure all the others have, but more often the not this is something which falls through with a vengeance. You MUST be aware of this. Turboing a car opens up a whole other can of worms. It will require a lot more maintenance as well as creating a shit ton of other potential issues/problems which you would never see on a non turbo car. This is compounded by the fact that these cars/engines were never meant to be boosted. So, even if you can afford the initial cost of purchasing and installing a turbo on your car, you might not be up to the task (both money and skill wise) of maintaining the car after its on. ESPECIALY if this is going to be your daily driver. You can expect the car to be out of commission for days at a time as you fix various problems that will probably come up as time goes on. And this is giving you the benefit of the doubt that you will get it 100% properly installed as well as getting quality (read: expensive) components.
This doesn’t even delve into the fact that kids with little to no experience piloting higher hp cars get into a LOT of trouble (and I don’t just mean tickets) with these types of vehicles. You will have major issues such as torque steer, understeer, loss of drive wheel traction, as well as highly shortened reaction times when driving these types of cars (and not even driving at the limit either). Furthermore, to HELP counteract SOME of these issues, more money must be spent on things such as brake, suspension, and tire upgrades. Those mods alone are going to run you more then the cost of the motor swap or the turbo kit, if done properly.
Basically, what I’m trying to say is that there is a much higher total cost to one of these cars then what you might think. It’s going to end up costing you a lot more in the end then the basic cost of the new engine/transmission & turbo kit. That’s 100% fact. Aside from money, there is a lot higher chance that you are going to either wreck your car and/or injure/kill yourself or someone else without proper driving experience and skill, no matter what mods you do to the vehicle.
My point is this. Listen carefully to what I just said and think about it really hard. You might be better off by going for an NA (naturally aspirated, AKA "all motor") build. You can get more than enough WHP to put a smile on your face by going this route, and it will allow you to build your skill and experience. It will also (on average) be a much more reliable and cost efficient method of modifying a car for daily driving duty. It’s a much simpler set up, meaning there are less things that can go wrong, and when they do go wrong it’s easier to diagnose and fix (not to mention cheaper for the most part). Lets also not forget that this will also be much more fuel efficient, because let’s face it, gas is only getting more expensive and you are going to need to start using PREMIUM gas. Plus I'm not even touching the whole smog legality issue!
For an all motor set up, I would suggest going with a B16A or B18C long block and mating it to a B16A transmission. You can have the head milled a little bit to up the CR as well as adding an aftermarket 2 layer head gasket to further bump the CR up. Combine this with basic bolt ons (intake/header/exhaust), add some cams & cam gears, then add a P28 ECU which has then been tuned and chipped on a dyno by a qualified tuner.
All of this will net you more than enough horse power to get you into trouble, and it will be a pretty straight forward yet very fun project. To top it off, you can keep adding things to further increase performance like a modified intake manifold, larger throttle body, phelonic spacers, etc, etc, etc.
Done right, after all is said and done, you can expect to see near, at or perhaps even over 200WHP. That’s more than enough go to get you into the 13s, which makes you faster than the majority of cars on the road today.
Of course, unless you plan on having a lot of money to throw at this whole shebang, you are going to need to make a decision as to which way you want to go BEFORE you start the project. Are you 100% SURE you want to go turbo, or do you think an NA build might be more your speed for now? This must be decided before even thinking of which motor to buy.
Take it from someone who has 10+ years of life and 13+ years of car building experience on you... that, my friend, is the most important decision that you are facing at the moment.