Moving a hard drive back and forth between computers?

Especially considering that for the price of 2 you could build one smaller and better.

1) Gaming - your best bet is to use STEAM then login when you move to your other computer. You'll have to download the games again (or make game BACKUPS and RESTORE those backups to the new computer).

2) DATA - depends on how much:
a) USB thumb drive (i.e. 128MB), or
b) USB HDD (i.e. 1TB), or
c) use the HDD for the new PC (internal drive), copy data to it, then move to new PC (i.e. as a secondary drive... this is a bit more complicated).

*For Steam, you could optionally just copy the entire "Steamapps" folder rather than create a backup. Install Steam on the new machine, then MOVE that entire folder to REPLACE the freshly created one (after you login).

SAVE GAMES are either on the cloud or in your "Documents", or "Documents-> My Games" folders usually. I pasted my saves back individually for non-cloud backups.

3) Laptop - for gaming, $700 is doable, but I'm not clear if the alternative is a $700 gaming rig for the second house. If so, then build a gaming rig using pcpartpicker (can shop around for Windows 10 license, as they can be cheaper).

Update: adding in the MONITOR is going to be problematic in terms of budget. I'll try to compare below anyway.

$800 laptop (over budget I know):
http://www.tomshardware.com/reviews/dell-inspiron-15-gaming-laptop,4446.html

I was looking at Bestbuy and other places and couldn't seem to find a half decent gaming laptop for $700. At least not what I consider good enough. I'll post that and see what I can build for $700 as a desktop (including monitor, Windows, mouse..).

Example PC build: http://pcpartpicker.com/p/jJkkFT

I tried to get close to $700USD, including monitor/Windows. I got close, but with no mouse/keyboard. Anyway, it's just an example. Some points:

a) mini-ITX motherboard (smaller)
b) chose 1x8GB (to add another identical stick later) due to limited mini-ITX slots

c) case - great case, there are smaller if need be
d) Monitor - possibly better but funds where limited

e) Windows - you can buy Windows 7 for $50 and use that to upgrade to Windows 10 (until July 29th 2016). I saw a copy on Amazon for "reburbished PC's" or something but should work fine.

Upgrading to W10 isn't too hard. In fact, you can burn an ISO from the MS site (ask more later if need be) and boot to it then just use the KEY from Windows 7. So you don't actually have to install Windows 7.

f) GPU - GTX750Ti is pretty good for about $120 budget.
g) *Motherboard - I chose the Asus motherboard because reviews/comments show that mini-ITX is rock solid. Well built. You do NOT want motherboard issues.

h) Wi-Fi - none, so get a USB stick if needed.
i) i3-4170 - this is IMO the best CPU for this budget. I do not recommend AMD.

Summary:
You can build a pretty nice computer for roughly $700. There are many different way to go (larger ATX, microATX), AMD CPU, cheap out on quality to get better GPU etc.

Again, as per my other comment (which you might want to SAVE), you can have STEAM running on two different computers using the same account, and even COPY the entire Steamapps folder so you don't need to save.

Final note.
If transporting the computer, pack and move carefully. Don't use large heat sinks. I would have recommended better than stock (for noise, not cooling) but it's something you can do later if you want. Do make sure to setup a CPU Fan profile regardless (should ramp up fan with temperature).

Update:
If you REMOVE the hard drive from your existing PC, you can then COPY the important data back over to the new one. Do NOT use it as a boot device. For example:
a) Build new PC, install Windows, drivers etc..
b) Steam - install and login (Blizzard games are also easy to COPY without downloading again. Google how)
c) PARTITION the hard drive (200GB for main Windows partition)
d) Create a Steam folder on 2nd partition (Steam settings...library folders). Such as "E:\Steam2"

e) Shut down, add drive from other PC
f) Bootup (if old drive is booted from, go into BIOS and switch back)
g) COPY the entire Steamapps folder to the 2nd partition folder for Steam
h) Start Steam or reboot if needed, then make sure games work (should verify game local content before launching... ask or google for how)

i) SAVE GAMES and other data - I'd just create a "from OLD PC" folder then copy the entire Documents folder into that. Then copy individual save games (after launching game once) back over. Not needed if Steamcloud has backup of save.

Summary:
I hope that helps more than confuses. Probably have questions but it should be a good start.