Trrjohn I would suggest you reconsider your punch list...
Nikon's most recent camera bodies (D5500 included) are able to use the new Pulse Stepper Motor focusing lenses...
There are two you should consider the AF-P DX Nikkor 70-300mm f/4.5-6.3G ED VR Lens
https://www.bhphotovideo.com/c/product/1275036-REG/nikon_20062_afp_dx_nikkor_70_300mm.htmlAnd the AF-P DX Nikkor 18-55mm f/3.5-5.6G VR
https://www.bhphotovideo.com/c/product/1275038-REG/nikon_20059_af_p_dx_nikkor_18_55mm.htmlBoth of these optics are so superior to the ones on your list that it would make little sense not to choose both of them instead...
The price point is actually less for both AF-P optics combined than either the 18-200mm or the 18-300mm
A major issue here is acuity... the new AF-P lenses are head and shoulders better... as is their Vibration Reduction... and they're feather light!
Best of all (for me at least) is the fact that they are virtually silent... I shoot video and this is a major game changer for Nikon...
How does Nikon achieve this high level of performance over the "Super Zooms" 18-200 and 18-300?
By using a much narrower zoom range (3X and 4X respectively for the AF-P optics) thus distortion/CA etc can be more effectively minimized.
Caveat: Be certain you choose the VR versions of these lenses... Nikon actually offers a non-VR version (cheaper) also...
Oh, you'll have to upgrade your camera's firmware to use these AF-P lenses...
btw, the close focus distance on the AF-P 18-55mm is a mere 9.8" which nearly eliminates the need for macro and/or extension tubes...
Also want to mention the lighting fast focus speed on the 70-300mm This was a shock! I'm amazed at the speed at which this tele locks focus... You will not believe AF speed until your try it... Seriously fast AF, it focuses as quick as my a Pro lenses... thank you Nikon!
Is there a down side? Yes the build quality is decidedly prosumer... they are delicate and will unlikely take much abuse...
That said if you are careful with your kit it should pose no problem... Still I would suggest not going for a cheaper "white box" deal and instead get the 5 year Nikon warranty... penny wise and pound foolish is a brutal lesson to learn...
Here is the link for your firmware upgrade
http://downloadcenter.nikonimglib.com/en/download/fw/176.htmlAnd what it will do for your D5500
Changes from “C” Firmware Version 1.00 to 1.01
• AF-P DX NIKKOR 18–55mm f/3.5–5.6G VR and AF-P DX NIKKOR 18–55mm f/3.5–5.6G lenses are now supported. Vibration reduction can be enabled or disabled using the new Optical VR option in the photo SHOOTING MENU, which is displayed when an AF-P DX NIKKOR 18–55mm f/3.5–5.6G VR lens is attached. The CUSTOM SETTING MENU now contains an a5 Manual focus ring in AF mode option that can be enabled or disabled when an AF-P DX NIKKOR 18–55mm f/3.5–5.6G VR or AF-P DX NIKKOR 18–55mm f/3.5–5.6G is attached.
Hope this helps or is at least food for thought
I wish you well on your journey Trrjohn