Unrelated but a tip for beginners from several lessons learned myself, When you get out of the water, always carry your board and don't let it float around you in knee deep water or less in the shorebreak. Most of my gashes, cuts & scrapes were from the board getting pushed into my ankles and feet in the shorebreak. Once you are coming in from a session and are in knee deep water, pick up your board. Will avoid you some cuts and bruises. Also for summer surfing you don't want your board hitting a little child which could be really bad situation as well.
I'll answer this a little different than everyone else. I don't have anywhere near the experience as a lot of these guys, so keep that in mind.
If you are old enough to be laid off, I gather that you aren't some 16 year old kid in the best shape of your life. I'm also going to assume that you probably don't live particularly near the ocean either. I could be wrong of course, and you could live a block away from the ocean and just decided to pick up surfing a little bit late. With that in mind, I'm not sure you are good to go with one lesson on a longboard/funboard and ready to move on to a shortboard.
It's true that water time is the most important thing, but I just don't see you getting a lot of water time. If you can't get to the ocean everytime there is swell, you probably aren't going to get enough practice on that board. On top of that, since you probably can't afford a wetsuit either, you are restricted to surfing basically the flattest months of the year.
I think some of it also depends on how far you've progressed. If you have been able to ride the face of a breaking wave, and maybe go down the line a bit, you'll have a better shot with the shortboard. But, if you are still riding the whitewater of unbroken waves, I think you are fighting an uphill battle. If that's the case, I think you are probably better off renting a funboard/longboard (it's like $15 for a day) a few more times until you get out of the whitewater. After that dedicate yourself to learning on the shortboard, which you'll probably be pretty happy with as you get the hang of it.