You'd be fine with the Mastermind. Assuming you're in a one-man SG, you'll have a bit of a slog ahead of you (rooms weigh in at 100,000 Prestige or so) but you'll be fine.
If you can make do with one room, just use the freebie entrace room and use your prestige to decorate it 
Remember that base rent is judged on the amount of Prestige in your bank, the number of functional items and the size of your base. So spend all your Prestige and rent should be good and low.
Yep, starter room with the portal in it costs you nothing, so you could just go ahead and move the portal to a corner then proceed to decorate to some extent. As the only person in your SG you'll eventually be able to build other rooms but we're talking quite some time here, also bear in mind that your level 38 will not gain influence whilst in SG mode, only prestige.
Alrightey, I'll just grind up to 100k prestige and go from there. 
At the moment, I just want to be capable of fiddling with something I call my own. I have well in excess of five million Infamy, so the Infamy hit won't really bother me that much (Especially seeing as you still get enhancements while in SG mode).
Thanks for the advice, guys.
Should try do what I did and get another player to help transfer all your alts into the SG. You may have to bribe them obviously but well worth it IMO. I started when I reached Lv10 and kept working from there and have >50K earned prestige from this (Lv21 now), the rest is from the alts joining the SG. If you're looking for a slow down starting another alt certainly couldn't hurt, just be patient.
Indeed, with a friend of mine, I've been able to fill a SG with atleast 15 members.
The resulting 300k prestige was enough to buy 2 rooms (2x2 controle room at 100k, and a 5x5 decorative room at 150k) and decorate them nicely.
That base is now the 'fudge base', most locations we need we can fudge, and RP in it accordingly.
Also, if you don't have so many alts free (which can happen) a trail code can be used.
I don't know if there's one for CoV, but most have one for CoH. (I know, not much help for you, but still...)
Just use names noone will ever pick (to bypass the 90 days name reservation time to longer) like... "Eressos temp alt 1" and so on, and fill them in the SG.
@ShadowGhost & @Ghostie
The Grav Mistress, Mistress of Gravity
If you have nothing useful to say, you have two choices: Say something useless or stay quiet.
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Remember that base rent is judged on the amount of Prestige in your bank, the number of functional items and the size of your base. So spend all your Prestige and rent should be good and low.
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Unless it's been changed and I missed it, rent should be based on the total amount of Prestige the SG has - regardless of whether its been spent on items, rooms and plots or is just sitting in the 'bank'.
This is to prevent rather obvious exploits like dismantling your base just before paying rent (if rent were based on the value of the base), or spending all your Prestige on base stuff just before paying the rent (if rent were based on 'unspent' Prestige).
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Yep, starter room with the portal in it costs you nothing, so you could just go ahead and move the portal to a corner then proceed to decorate to some extent. As the only person in your SG you'll eventually be able to build other rooms but we're talking quite some time here, also bear in mind that your level 38 will not gain influence whilst in SG mode, only prestige.
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The problem with moving the portal is that if theres items near it you could get stuck entering the base. I had this happen in beta and here and now goonie portal is at center of room all by itself. That makes the room all that much smaller really.
Little point on prestige is that since I joined ARAD I have earned about 100k prestige in 20 days with my lvl 33 MM. So with your 38 you should be raking in about 5k a day if you play alot which I tend to do so say a month to get the prestige you need for min base.
Ok, I've been tossing around this idea for a bit, but a recent need to just kick back and slow down has made me want to put this into plan.
Let's say I just wanted to mess around and make a pretty looking room or two; none of the mod cons such as teleporters and revolving gatlin cannons, but a little something to just mess about in.
Now let's say I'd be the only one getting the Prestige together.
If it's even feasible - unlikely, but I hope - would it be better for me to farm Prestige with a level 38 Mastermind, or start an alt and run her in SG mode constantly?
Just a random little thing I've been thinking about, as I said, so it's not something that's incredibly important.