Just started going to the gym again

So I slacked off this year big time. Its been four or five months since I've been to the gym other than a few tennis or basketball matches here and there and the result is im way out of shape and it feels like im a beginner again. So im dedicated to getting back to work for the next six months.

Anyway, i've always had cardio problems when I push myself, even when im in shape, but its downright ridiculous atm.

I do about a 20 minute cardio routine where I do wind sprints, then jog, wind sprints then jog.

The problem is after that I have almost no energy for weights. After the first few reps, on any muscle group, im gassing bad. So much so that I couldn't even do ten pullups without sucking wind. I'm not even getting a burn in the muscles, which means I think that my bottleneck is that im not getting enough oxygen to my muscles.

What sort of routine should I do for the next say 2 weeks so that I get at least some benefit and get my body functioning for the gym again? How many times a week should I go? How long should I cardio, and what sort of intensity?

I'm not an expert, take this with a grain of salt, I don't even go to a gym.

I've read that you should do your resistance workout first, and then your cardio. I don't have the source, that's just from memory somewhere.

uh don't do heavy cardio same day as lifting... definitely not right before lifting. i'm dead after cardio, last thing I want to do is lift weights

alternate days between cardio and lifting weights until you feel more in shape

honestly though i don't get how people are able to do cardio and weights on the same day right before or after one another. i could do something like run in the morning and lift in the evening... but no way in hell could i run for half an hour then start lifting weights. doesn't make sense to me

I used to do cardio for a half hour before lifting when I was trying to cut. In retrospect I think it did more harm than good. If you are going to do them on the same day and still looking to gain any significant muscle I'd recommend doing cardio after. Really though I would do like confidential said and either split up days or put them on opposite ends of the days.

You should really state whether you're trying to lose weight or build muscle as that is somewhat critical to what gameplan you should take.

I do 45 minutes of cardio every day I lift.

I want to gain core and functional muscle, as well as to simply get in shape to restart Jitsu training (which has reopened recently, hence the motivation). I don't have much fat on my body (atm im hovering around ~12% bodyfat as measured by the electro test, which is more or less my natural state).

I can do cardio another day, but I have a feeling i'd still gas a little bit into the weight workout. I'm breathing heavy, but I get the feeling oxygen is not going to the muscles and hence the recuperation period after a set is painfully long. Hence the reason i've been doing a lot of cardio, so that I actually have the stamina to get a good workout.

I've never not done cardio before weights. Every trainer i've ever had has always insisted on that 15-20 minute warmup. I don't know why.

So I slacked off this year big time. Its been four or five months since I've been to the gym other than a few tennis or basketball matches here and there and the result is im way out of shape and it feels like im a beginner again. So im dedicated to getting back to work for the next six months.

Anyway, i've always had cardio problems when I push myself, even when im in shape, but its downright ridiculous atm.

I do about a 20 minute cardio routine where I do wind sprints, then jog, wind sprints then jog.

The problem is after that I have almost no energy for weights. After the first few reps, on any muscle group, im gassing bad. So much so that I couldn't even do ten pullups without sucking wind. I'm not even getting a burn in the muscles, which means I think that my bottleneck is that im not getting enough oxygen to my muscles.

What sort of routine should I do for the next say 2 weeks so that I get at least some benefit and get my body functioning for the gym again? How many times a week should I go? How long should I cardio, and what sort of intensity?

man if i tried to lift weights after doing 20 minutes of sprinting i'd just pack my shit and go home

you should probably not do a heavy cardio session immediately before a weight session especially if you're as untrained as you say

warmups are great and all and i'm sure you can go heavy on both on the same day but only after you're already at a baseline of fitness

sometimes less is more. the last thing you want to do is overtraining: it stops your progress and you'll feel like shit.
you really don't have to weight train more than 2-3x a week if you're eating properly (rippetoe's program is 3x a week, and that works great for a lot of people). Try alternating cardio and lifting days.
I'm not a cardio expert, so I can't give any advice I wouldn't take with a grain of salt, but doing HIIT or 30-45 minutes of running should be fine to increase your cardio (might want to start doing less if you're out of shape and build up to that). As for weight training, definitely do squats, deadlifts, and power cleans at the very least. Those exercises are fantastic for just about everyone, especially at developing the core and back muscles you'll need for jits. As far as doing cardio before working out, I usually warm up for 5 or 6 minutes doing light cardio to get my heart rate up and then do some dynamic stretches before I lift. Doing 20 minutes as a warmup seems kind of excessive to me.
But like I said, I'm no expert, and if anybody with more experience can correct me you should probably listen to them, but that's my thoughts on it.

I want to gain core and functional muscle, as well as to simply get in shape to restart Jitsu training (which has reopened recently, hence the motivation). I don't have much fat on my body (atm im hovering around ~12% bodyfat as measured by the electro test, which is more or less my natural state).

I can do cardio another day, but I have a feeling i'd still gas a little bit into the weight workout. I'm breathing heavy, but I get the feeling oxygen is not going to the muscles and hence the recuperation period after a set is painfully long. Hence the reason i've been doing a lot of cardio, so that I actually have the stamina to get a good workout.

I've never not done cardio before weights. Every trainer i've ever had has always insisted on that 15-20 minute warmup. I don't know why.

That's odd. I'm currently working out with a professional and competitive body builder and we never do more than a 10-minute warmup just to open up the lungs and get started. He's always stressed resistance training before cardio and that's all I've ever heard prior to partnering up with him as well.

It sounds like you don't have any muscle endurance if you're getting gassed early on. It also probably has to do with cardio prior to your workout. Go for proper form, low(er) weight, and sets of 12 to 15 reps instead of whatever you're doing (I'm assuming 10 or lower). Do whatever you want after you get adjusted.