I was planning to use either 144 or 440 band for my repeater
OK.
On the 2 meter band, standard* repeater offset is 600KHz. Depending on which frequency you pick, your input would either be 600KHz above or 600KHz below the output.
On the 70 centimeter band, standard* repeater offset is 5MHz. That can either be 5MHz above or below depending on the coordinator.
You'll have more room to work and more separation between your frequencies if you do this on the 70cm band.
and it would be one of those lunchbox types so I didn't think it would require coordination.
OK, look at your local bandplans (search on repeater listings for your state) and see if they have any temporary repeater pairs set aside, or 'test' pairs you can use for this.
As for everything else, people are mostly trying to help you. This repeater, as you have it planned, is not going to work well, if at all. The transmitter will be too close to the receiver and it'll overload it, making the repeater deaf and providing range measured in feet or yards. Worst case, transmitting at full power right next to a receiver can damage the receiver. $20 radio, so no big loss, but learn from the mistakes of others.
Lots of TX and RX antenna separation will help a bit, but range is going to be exceedingly short.
The duplexer is the right tool for the job, but those are a complex device and take some good test equipment to set up.
Doing a cross band repeater, as in an input on 2 meter band and an output on 70 centimeters will give you better performance and might actually work well enough to be useful. But, still, keep your TX and RX separated by a few feet to keep from hurting the radio.
This will be a good experiment to learn some new things, but don't expect this to be a long range repeater. This is a hobby, and a place to play, so go for it, but don't expect a miracle out of this setup.
* Regarding the use of the term "standard":
"The nice thing about standards is that there are so many to choose from." This is where frequency coordination comes in. Making sure your repeater gets along with all the others. You do not want your repeater output transmitting on the input of another. Playing well with others is part of the hobby. If you are not going to coordinate, then make sure you keep any emissions inside the amateur radio band, and you don't annoy other users. Hams can be a cranky and vengeful lot. You can use different input/output offsets to help your lack of duplexer, but you'll not get enough spacing to make a real difference. For short tests, you'll likely not upset other hams, but if you plan on playing with this long term, make sure you pay close attention to the established band plans and you are not stepping on satellite sub bands, CW, SSB, or other slices of dedicated spectrum.